## Defining parameters

Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |

Weight: | \( k \) | \(=\) | \( 9 \) |

Character orbit: | \([\chi]\) | \(=\) | 16.d (of order \(2\) and degree \(1\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |

Character field: | \(\Q\) | ||

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

Sturm bound: | \(18\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(16, [\chi])\).

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

Modular forms | 18 | 0 | 18 |

Cusp forms | 14 | 0 | 14 |

Eisenstein series | 4 | 0 | 4 |

## Decomposition of \(S_{9}^{\mathrm{old}}(16, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(16, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 2}\)