## Defining parameters

Level: | \( N \) | = | \( 4019 \) |

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

Nonzero newspaces: | \( 6 \) | ||

Sturm bound: | \(2692060\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4019))\).

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

Modular forms | 675024 | 675024 | 0 |

Cusp forms | 671007 | 671007 | 0 |

Eisenstein series | 4017 | 4017 | 0 |

## Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4019))\)

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

4019.2.a | \(\chi_{4019}(1, \cdot)\) | 4019.2.a.a | 149 | 1 |

4019.2.a.b | 186 | |||

4019.2.c | \(\chi_{4019}(273, \cdot)\) | n/a | 2004 | 6 |

4019.2.e | \(\chi_{4019}(48, \cdot)\) | n/a | 13360 | 40 |

4019.2.f | \(\chi_{4019}(3, \cdot)\) | n/a | 14028 | 42 |

4019.2.i | \(\chi_{4019}(20, \cdot)\) | n/a | 80160 | 240 |

4019.2.k | \(\chi_{4019}(4, \cdot)\) | n/a | 561120 | 1680 |

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