## Defining parameters

Level: | \( N \) | \(=\) | \( 52 = 2^{2} \cdot 13 \) |

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

Character orbit: | \([\chi]\) | \(=\) | 52.d (of order \(2\) and degree \(1\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |

Character field: | \(\Q\) | ||

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

Sturm bound: | \(14\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(52, [\chi])\).

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

Modular forms | 10 | 0 | 10 |

Cusp forms | 4 | 0 | 4 |

Eisenstein series | 6 | 0 | 6 |

## Decomposition of \(S_{2}^{\mathrm{old}}(52, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(52, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)