Properties

Label 394.3
Level 394
Weight 3
Dimension 3234
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 29106
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 394 = 2 \cdot 197 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(29106\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(394))\).

Total New Old
Modular forms 9898 3234 6664
Cusp forms 9506 3234 6272
Eisenstein series 392 0 392

Trace form

\( 3234 q + O(q^{10}) \) \( 3234 q + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(394))\)

We only show spaces with odd 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
394.3.c \(\chi_{394}(183, \cdot)\) 394.3.c.a 32 2
394.3.c.b 34
394.3.f \(\chi_{394}(69, \cdot)\) 394.3.f.a 192 12
394.3.f.b 204
394.3.i \(\chi_{394}(3, \cdot)\) 394.3.i.a 1344 84
394.3.i.b 1428

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(394))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(394)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(197))\)\(^{\oplus 2}\)