Defining parameters
Level: | \( N \) | = | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 17 \) | ||
Sturm bound: | \(2304\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(72))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1056 | 459 | 597 |
Cusp forms | 960 | 441 | 519 |
Eisenstein series | 96 | 18 | 78 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(72))\)
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 |
---|---|---|---|---|
72.8.a | \(\chi_{72}(1, \cdot)\) | 72.8.a.a | 1 | 1 |
72.8.a.b | 1 | |||
72.8.a.c | 1 | |||
72.8.a.d | 1 | |||
72.8.a.e | 1 | |||
72.8.a.f | 2 | |||
72.8.a.g | 2 | |||
72.8.c | \(\chi_{72}(71, \cdot)\) | None | 0 | 1 |
72.8.d | \(\chi_{72}(37, \cdot)\) | 72.8.d.a | 2 | 1 |
72.8.d.b | 6 | |||
72.8.d.c | 12 | |||
72.8.d.d | 14 | |||
72.8.f | \(\chi_{72}(35, \cdot)\) | 72.8.f.a | 28 | 1 |
72.8.i | \(\chi_{72}(25, \cdot)\) | 72.8.i.a | 20 | 2 |
72.8.i.b | 22 | |||
72.8.l | \(\chi_{72}(11, \cdot)\) | 72.8.l.a | 4 | 2 |
72.8.l.b | 160 | |||
72.8.n | \(\chi_{72}(13, \cdot)\) | 72.8.n.a | 164 | 2 |
72.8.o | \(\chi_{72}(23, \cdot)\) | None | 0 | 2 |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(72))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(72)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)