Defining parameters
Level: | \( N \) | = | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 38 \) | ||
Sturm bound: | \(17496\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(324))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6102 | 2744 | 3358 |
Cusp forms | 5562 | 2632 | 2930 |
Eisenstein series | 540 | 112 | 428 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(324))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
324.3.c | \(\chi_{324}(161, \cdot)\) | 324.3.c.a | 4 | 1 |
324.3.c.b | 4 | |||
324.3.d | \(\chi_{324}(163, \cdot)\) | 324.3.d.a | 2 | 1 |
324.3.d.b | 2 | |||
324.3.d.c | 2 | |||
324.3.d.d | 2 | |||
324.3.d.e | 6 | |||
324.3.d.f | 6 | |||
324.3.d.g | 8 | |||
324.3.d.h | 8 | |||
324.3.d.i | 8 | |||
324.3.f | \(\chi_{324}(55, \cdot)\) | 324.3.f.a | 2 | 2 |
324.3.f.b | 2 | |||
324.3.f.c | 2 | |||
324.3.f.d | 2 | |||
324.3.f.e | 2 | |||
324.3.f.f | 2 | |||
324.3.f.g | 2 | |||
324.3.f.h | 2 | |||
324.3.f.i | 2 | |||
324.3.f.j | 2 | |||
324.3.f.k | 4 | |||
324.3.f.l | 4 | |||
324.3.f.m | 4 | |||
324.3.f.n | 4 | |||
324.3.f.o | 8 | |||
324.3.f.p | 8 | |||
324.3.f.q | 12 | |||
324.3.f.r | 12 | |||
324.3.f.s | 16 | |||
324.3.g | \(\chi_{324}(53, \cdot)\) | 324.3.g.a | 2 | 2 |
324.3.g.b | 2 | |||
324.3.g.c | 4 | |||
324.3.g.d | 8 | |||
324.3.j | \(\chi_{324}(19, \cdot)\) | 324.3.j.a | 204 | 6 |
324.3.k | \(\chi_{324}(17, \cdot)\) | 324.3.k.a | 36 | 6 |
324.3.n | \(\chi_{324}(7, \cdot)\) | 324.3.n.a | 1908 | 18 |
324.3.o | \(\chi_{324}(5, \cdot)\) | 324.3.o.a | 324 | 18 |
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)