## Defining parameters

Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |

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

Character orbit: | \([\chi]\) | \(=\) | 441.x (of order \(14\) and degree \(6\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 147 \) |

Character field: | \(\Q(\zeta_{14})\) | ||

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

Sturm bound: | \(56\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(441, [\chi])\).

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

Modular forms | 36 | 0 | 36 |

Cusp forms | 12 | 0 | 12 |

Eisenstein series | 24 | 0 | 24 |

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 |

## Decomposition of \(S_{1}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)