Defining parameters
Level: | \( N \) | = | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(52488\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(324))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 23598 | 10808 | 12790 |
Cusp forms | 23058 | 10696 | 12362 |
Eisenstein series | 540 | 112 | 428 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(324))\)
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 |
---|---|---|---|---|
324.9.c | \(\chi_{324}(161, \cdot)\) | 324.9.c.a | 16 | 1 |
324.9.c.b | 16 | |||
324.9.d | \(\chi_{324}(163, \cdot)\) | n/a | 188 | 1 |
324.9.f | \(\chi_{324}(55, \cdot)\) | n/a | 380 | 2 |
324.9.g | \(\chi_{324}(53, \cdot)\) | 324.9.g.a | 2 | 2 |
324.9.g.b | 2 | |||
324.9.g.c | 4 | |||
324.9.g.d | 4 | |||
324.9.g.e | 4 | |||
324.9.g.f | 4 | |||
324.9.g.g | 12 | |||
324.9.g.h | 32 | |||
324.9.j | \(\chi_{324}(19, \cdot)\) | n/a | 852 | 6 |
324.9.k | \(\chi_{324}(17, \cdot)\) | n/a | 144 | 6 |
324.9.n | \(\chi_{324}(7, \cdot)\) | n/a | 7740 | 18 |
324.9.o | \(\chi_{324}(5, \cdot)\) | n/a | 1296 | 18 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 1}\)