Defining parameters
Level: | \( N \) | = | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(23328\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(324))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9018 | 4088 | 4930 |
Cusp forms | 8478 | 3976 | 4502 |
Eisenstein series | 540 | 112 | 428 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(324))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
324.4.a | \(\chi_{324}(1, \cdot)\) | 324.4.a.a | 1 | 1 |
324.4.a.b | 1 | |||
324.4.a.c | 3 | |||
324.4.a.d | 3 | |||
324.4.a.e | 4 | |||
324.4.b | \(\chi_{324}(323, \cdot)\) | 324.4.b.a | 4 | 1 |
324.4.b.b | 8 | |||
324.4.b.c | 24 | |||
324.4.b.d | 32 | |||
324.4.e | \(\chi_{324}(109, \cdot)\) | 324.4.e.a | 2 | 2 |
324.4.e.b | 2 | |||
324.4.e.c | 2 | |||
324.4.e.d | 2 | |||
324.4.e.e | 2 | |||
324.4.e.f | 2 | |||
324.4.e.g | 2 | |||
324.4.e.h | 2 | |||
324.4.e.i | 8 | |||
324.4.h | \(\chi_{324}(107, \cdot)\) | n/a | 140 | 2 |
324.4.i | \(\chi_{324}(37, \cdot)\) | 324.4.i.a | 54 | 6 |
324.4.l | \(\chi_{324}(35, \cdot)\) | n/a | 312 | 6 |
324.4.m | \(\chi_{324}(13, \cdot)\) | n/a | 486 | 18 |
324.4.p | \(\chi_{324}(11, \cdot)\) | n/a | 2880 | 18 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 1}\)