## Defining parameters

Level: | \( N \) | = | \( 4027 \) |

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

Nonzero newspaces: | \( 8 \) | ||

Sturm bound: | \(2702788\) |

## Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4027))\).

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

Modular forms | 677710 | 677710 | 0 |

Cusp forms | 673685 | 673685 | 0 |

Eisenstein series | 4025 | 4025 | 0 |

## Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4027))\)

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 |
---|---|---|---|---|

4027.2.a | \(\chi_{4027}(1, \cdot)\) | 4027.2.a.a | 2 | 1 |

4027.2.a.b | 159 | |||

4027.2.a.c | 174 | |||

4027.2.c | \(\chi_{4027}(1820, \cdot)\) | n/a | 670 | 2 |

4027.2.e | \(\chi_{4027}(14, \cdot)\) | n/a | 3340 | 10 |

4027.2.g | \(\chi_{4027}(130, \cdot)\) | n/a | 6700 | 20 |

4027.2.h | \(\chi_{4027}(13, \cdot)\) | n/a | 20040 | 60 |

4027.2.k | \(\chi_{4027}(41, \cdot)\) | n/a | 40200 | 120 |

4027.2.m | \(\chi_{4027}(4, \cdot)\) | n/a | 200400 | 600 |

4027.2.o | \(\chi_{4027}(6, \cdot)\) | n/a | 402000 | 1200 |

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