Defining parameters
Level: | \( N \) | = | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 9 \) | ||
Newform subspaces: | \( 36 \) | ||
Sturm bound: | \(60000\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(750))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15720 | 3456 | 12264 |
Cusp forms | 14281 | 3456 | 10825 |
Eisenstein series | 1439 | 0 | 1439 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)
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 |
---|---|---|---|---|
750.2.a | \(\chi_{750}(1, \cdot)\) | 750.2.a.a | 2 | 1 |
750.2.a.b | 2 | |||
750.2.a.c | 2 | |||
750.2.a.d | 2 | |||
750.2.a.e | 2 | |||
750.2.a.f | 2 | |||
750.2.a.g | 2 | |||
750.2.a.h | 2 | |||
750.2.c | \(\chi_{750}(499, \cdot)\) | 750.2.c.a | 4 | 1 |
750.2.c.b | 4 | |||
750.2.c.c | 4 | |||
750.2.c.d | 4 | |||
750.2.e | \(\chi_{750}(443, \cdot)\) | 750.2.e.a | 32 | 2 |
750.2.e.b | 32 | |||
750.2.g | \(\chi_{750}(151, \cdot)\) | 750.2.g.a | 4 | 4 |
750.2.g.b | 4 | |||
750.2.g.c | 8 | |||
750.2.g.d | 8 | |||
750.2.g.e | 8 | |||
750.2.g.f | 16 | |||
750.2.g.g | 16 | |||
750.2.h | \(\chi_{750}(49, \cdot)\) | 750.2.h.a | 8 | 4 |
750.2.h.b | 8 | |||
750.2.h.c | 8 | |||
750.2.h.d | 16 | |||
750.2.h.e | 16 | |||
750.2.l | \(\chi_{750}(107, \cdot)\) | 750.2.l.a | 80 | 8 |
750.2.l.b | 80 | |||
750.2.l.c | 80 | |||
750.2.m | \(\chi_{750}(31, \cdot)\) | 750.2.m.a | 100 | 20 |
750.2.m.b | 120 | |||
750.2.m.c | 120 | |||
750.2.m.d | 140 | |||
750.2.o | \(\chi_{750}(19, \cdot)\) | 750.2.o.a | 240 | 20 |
750.2.o.b | 280 | |||
750.2.r | \(\chi_{750}(17, \cdot)\) | 750.2.r.a | 2000 | 40 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(750))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(750)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 2}\)