## Defining parameters

Level: | \( N \) | = | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |

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

Character orbit: | \([\chi]\) | = | 9450.fk (of order \(45\) and degree \(24\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 4725 \) |

Character field: | \(\Q(\zeta_{45})\) | ||

Sturm bound: | \(4320\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(9450, [\chi])\).

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

Modular forms | 52032 | 17280 | 34752 |

Cusp forms | 51648 | 17280 | 34368 |

Eisenstein series | 384 | 0 | 384 |

## Decomposition of \(S_{2}^{\mathrm{new}}(9450, [\chi])\) into irreducible Hecke orbits

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

## Decomposition of \(S_{2}^{\mathrm{old}}(9450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(9450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4725, [\chi])\)\(^{\oplus 2}\)