## Defining parameters

Level: | \( N \) | = | \( 6047 \) |

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

Nonzero newspaces: | \( 2 \) | ||

Sturm bound: | \(6094368\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6047))\).

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

Modular forms | 1526615 | 1526615 | 0 |

Cusp forms | 1520570 | 1520570 | 0 |

Eisenstein series | 6045 | 6045 | 0 |

## Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6047))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|

6047.2.a | \(\chi_{6047}(1, \cdot)\) | 6047.2.a.a | 217 | 1 |

6047.2.a.b | 287 | |||

6047.2.c | \(\chi_{6047}(2, \cdot)\) | n/a | 1520066 | 3022 |

"n/a" means that newforms for that character have not been added to the database yet