## Defining parameters

Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |

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

Character orbit: | \([\chi]\) | \(=\) | 5520.fn (of order \(44\) and degree \(20\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1840 \) |

Character field: | \(\Q(\zeta_{44})\) | ||

Sturm bound: | \(2304\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5520, [\chi])\).

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

Modular forms | 23200 | 11520 | 11680 |

Cusp forms | 22880 | 11520 | 11360 |

Eisenstein series | 320 | 0 | 320 |

## Decomposition of \(S_{2}^{\mathrm{new}}(5520, [\chi])\) into newform subspaces

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

## Decomposition of \(S_{2}^{\mathrm{old}}(5520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1840, [\chi])\)\(^{\oplus 2}\)