## Defining parameters

Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |

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

Character orbit: | \([\chi]\) | \(=\) | 608.o (of order \(6\) and degree \(2\)) |

Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 152 \) |

Character field: | \(\Q(\zeta_{6})\) | ||

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

Sturm bound: | \(80\) | ||

Trace bound: | \(0\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(608, [\chi])\).

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

Modular forms | 24 | 6 | 18 |

Cusp forms | 8 | 2 | 6 |

Eisenstein series | 16 | 4 | 12 |

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

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

Dimension | 2 | 0 | 0 | 0 |

## Trace form

## Decomposition of \(S_{1}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|

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

608.1.o.a | $2$ | $0.303$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-1\) | \(0\) | \(0\) | \(q+\zeta_{6}^{2}q^{3}+q^{11}+\zeta_{6}^{2}q^{17}+\zeta_{6}q^{19}+\cdots\) |

## Decomposition of \(S_{1}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)