## Defining parameters

Level: | \( N \) | = | \( 800 = 2^{5} \cdot 5^{2} \) |

Weight: | \( k \) | = | \( 1 \) |

Character orbit: | \([\chi]\) | = | 800.bv (of order \(20\) and degree \(8\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 400 \) |

Character field: | \(\Q(\zeta_{20})\) | ||

Newforms: | \( 0 \) | ||

Sturm bound: | \(120\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(800, [\chi])\).

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

Modular forms | 32 | 0 | 32 |

Cusp forms | 0 | 0 | 0 |

Eisenstein series | 32 | 0 | 32 |

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|

Dimension | 0 | 0 | 0 | 0 |