## Defining parameters

Level: | \( N \) | = | \( 288 = 2^{5} \cdot 3^{2} \) |

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

Character orbit: | \([\chi]\) | = | 288.y (of order \(12\) and degree \(4\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 144 \) |

Character field: | \(\Q(\zeta_{12})\) | ||

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

Sturm bound: | \(96\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

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

Modular forms | 208 | 0 | 208 |

Cusp forms | 176 | 0 | 176 |

Eisenstein series | 32 | 0 | 32 |

## Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)