## Defining parameters

Level: | \( N \) | = | \( 4003 \) |

Weight: | \( k \) | = | \( 2 \) |

Nonzero newspaces: | \( 8 \) | ||

Sturm bound: | \(2670668\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4003))\).

Total | New | Old | |
---|---|---|---|

Modular forms | 669668 | 669668 | 0 |

Cusp forms | 665667 | 665667 | 0 |

Eisenstein series | 4001 | 4001 | 0 |

## Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4003))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|

4003.2.a | \(\chi_{4003}(1, \cdot)\) | 4003.2.a.a | 2 | 1 |

4003.2.a.b | 152 | |||

4003.2.a.c | 179 | |||

4003.2.c | \(\chi_{4003}(822, \cdot)\) | n/a | 666 | 2 |

4003.2.e | \(\chi_{4003}(551, \cdot)\) | n/a | 7304 | 22 |

4003.2.f | \(\chi_{4003}(102, \cdot)\) | n/a | 9296 | 28 |

4003.2.i | \(\chi_{4003}(129, \cdot)\) | n/a | 14652 | 44 |

4003.2.j | \(\chi_{4003}(10, \cdot)\) | n/a | 18648 | 56 |

4003.2.m | \(\chi_{4003}(6, \cdot)\) | n/a | 204512 | 616 |

4003.2.o | \(\chi_{4003}(4, \cdot)\) | n/a | 410256 | 1232 |

"n/a" means that newforms for that character have not been added to the database yet