Login System

Hi, I am new in Drupal module development.
I am trying to make a login system that looks like the one on drupal forum. I have used the form API and I want to display the login form with the hook_menu() function so that it shows in a page. But the page could not be found, This is what I have done:

<?php

// $Id$

/**
* @file
* Module for showing Login system form and display it through a URL or path.
*/

/**
* First I create a menu to display the login form
* Implements hook_menu() to create a URL for the login form.
*/
function user_menu() {
$items['userlogin'] = array(
'title' => t('Login System'),
'page callback' => 'drupal_get_form',
'page arguments' => array('user_login'),
'access callback' => TRUE,
);
return $items;
}

/**
* use hook_login() to display the login form
*
*
*/
function user_login($form, &$form_state) {
global $user;

// If already logged on, go to the user page instead.
if ($user->uid) {
drupal_goto('user/' . $user->uid);
}

// Display login form:
$form['name'] = array(
'#type' => 'textfield',
'#title' => t('Dispaly Name'),
'#size' => 60,
'#maxlength' => USERNAME_MAX_LENGTH,
'#required' => TRUE,
);

$form['name']['#description'] = t('Enter your @s username.', array('@s' => variable_get('site_name', 'Drupal')));
$form['pass'] = array(
'#type' => 'password',
'#title' => t('Password'),
'#description' => t('Enter password.'),
'#required' => TRUE,
);
$form['#validate'] = user_login_default_validators();
$form['actions'] = array('#type' => 'actions');
$form['actions']['submit'] = array(
'#type' => 'submit',
'#value' => t('Log in'),
);

return $form;
}

I have named the module: user.module
Is there something I am not doing right?