## Defining parameters

Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |

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

Character orbit: | \([\chi]\) | \(=\) | 4032.fb (of order \(16\) and degree \(8\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 448 \) |

Character field: | \(\Q(\zeta_{16})\) | ||

Sturm bound: | \(1536\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4032, [\chi])\).

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

Modular forms | 6208 | 2576 | 3632 |

Cusp forms | 6080 | 2544 | 3536 |

Eisenstein series | 128 | 32 | 96 |

## Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of \(S_{2}^{\mathrm{old}}(4032, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)