## Defining parameters

Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |

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

Character orbit: | \([\chi]\) | \(=\) | 3969.bt (of order \(42\) and degree \(12\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 441 \) |

Character field: | \(\Q(\zeta_{42})\) | ||

Newform subspaces: | \( 1 \) | ||

Sturm bound: | \(504\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3969, [\chi])\).

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

Modular forms | 156 | 36 | 120 |

Cusp forms | 12 | 12 | 0 |

Eisenstein series | 144 | 24 | 120 |

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|

Dimension | 12 | 0 | 0 | 0 |

## Trace form

## Decomposition of \(S_{1}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces

Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|

$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||

3969.1.bt.a | $12$ | $1.981$ | \(\Q(\zeta_{21})\) | $D_{7}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(q-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+(\zeta_{42}^{8}-\zeta_{42}^{17}+\cdots)q^{13}+\cdots\) |