## Defining parameters

Level: | \( N \) | = | \( 4013 \) |

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

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

Sturm bound: | \(2684028\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4013))\).

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

Modular forms | 673013 | 673013 | 0 |

Cusp forms | 669002 | 669002 | 0 |

Eisenstein series | 4011 | 4011 | 0 |

## Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4013))\)

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 |
---|---|---|---|---|

4013.2.a | \(\chi_{4013}(1, \cdot)\) | 4013.2.a.a | 1 | 1 |

4013.2.a.b | 157 | |||

4013.2.a.c | 176 | |||

4013.2.b | \(\chi_{4013}(4012, \cdot)\) | n/a | 334 | 1 |

4013.2.d | \(\chi_{4013}(53, \cdot)\) | n/a | 5328 | 16 |

4013.2.e | \(\chi_{4013}(10, \cdot)\) | n/a | 5344 | 16 |

4013.2.f | \(\chi_{4013}(40, \cdot)\) | n/a | 19314 | 58 |

4013.2.h | \(\chi_{4013}(114, \cdot)\) | n/a | 19372 | 58 |

4013.2.j | \(\chi_{4013}(7, \cdot)\) | n/a | 309024 | 928 |

4013.2.k | \(\chi_{4013}(4, \cdot)\) | n/a | 309952 | 928 |

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