## Defining parameters

Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |

Weight: | \( k \) | \(=\) | \( 3 \) |

Character orbit: | \([\chi]\) | \(=\) | 1152.bo (of order \(48\) and degree \(16\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 576 \) |

Character field: | \(\Q(\zeta_{48})\) | ||

Newform subspaces: | \( 0 \) | ||

Sturm bound: | \(576\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).

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

Modular forms | 6208 | 0 | 6208 |

Cusp forms | 6080 | 0 | 6080 |

Eisenstein series | 128 | 0 | 128 |

## Decomposition of \(S_{3}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)