## Defining parameters

Level: | \( N \) | = | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |

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

Character orbit: | \([\chi]\) | = | 7623.bs (of order \(10\) and degree \(4\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 231 \) |

Character field: | \(\Q(\zeta_{10})\) | ||

Sturm bound: | \(2112\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7623, [\chi])\).

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

Modular forms | 4416 | 1152 | 3264 |

Cusp forms | 4032 | 1152 | 2880 |

Eisenstein series | 384 | 0 | 384 |

## Decomposition of \(S_{2}^{\mathrm{new}}(7623, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of \(S_{2}^{\mathrm{old}}(7623, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7623, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2541, [\chi])\)\(^{\oplus 2}\)