## Defining parameters

Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |

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

Character orbit: | \([\chi]\) | \(=\) | 208.f (of order \(2\) and degree \(1\)) |

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

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

Newform subspaces: | \( 2 \) | ||

Sturm bound: | \(56\) | ||

Trace bound: | \(1\) | ||

Distinguishing \(T_p\): | \(3\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(208, [\chi])\).

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

Modular forms | 34 | 8 | 26 |

Cusp forms | 22 | 6 | 16 |

Eisenstein series | 12 | 2 | 10 |

## Trace form

## Decomposition of \(S_{2}^{\mathrm{new}}(208, [\chi])\) into newform subspaces

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

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

208.2.f.a | $2$ | $1.661$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}+iq^{5}+iq^{7}-2q^{9}+(2-i)q^{13}+\cdots\) |

208.2.f.b | $4$ | $1.661$ | \(\Q(i, \sqrt{17})\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\) |

## Decomposition of \(S_{2}^{\mathrm{old}}(208, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(208, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)