Defining parameters
Level: | \( N \) | = | \( 512 = 2^{9} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 7 \) | ||
Newform subspaces: | \( 34 \) | ||
Sturm bound: | \(32768\) | ||
Trace bound: | \(9\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(512))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8576 | 4720 | 3856 |
Cusp forms | 7809 | 4496 | 3313 |
Eisenstein series | 767 | 224 | 543 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)
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 |
---|---|---|---|---|
512.2.a | \(\chi_{512}(1, \cdot)\) | 512.2.a.a | 2 | 1 |
512.2.a.b | 2 | |||
512.2.a.c | 2 | |||
512.2.a.d | 2 | |||
512.2.a.e | 2 | |||
512.2.a.f | 2 | |||
512.2.a.g | 4 | |||
512.2.b | \(\chi_{512}(257, \cdot)\) | 512.2.b.a | 2 | 1 |
512.2.b.b | 2 | |||
512.2.b.c | 4 | |||
512.2.b.d | 4 | |||
512.2.b.e | 4 | |||
512.2.e | \(\chi_{512}(129, \cdot)\) | 512.2.e.a | 2 | 2 |
512.2.e.b | 2 | |||
512.2.e.c | 2 | |||
512.2.e.d | 2 | |||
512.2.e.e | 2 | |||
512.2.e.f | 2 | |||
512.2.e.g | 2 | |||
512.2.e.h | 2 | |||
512.2.e.i | 8 | |||
512.2.e.j | 8 | |||
512.2.g | \(\chi_{512}(65, \cdot)\) | 512.2.g.a | 4 | 4 |
512.2.g.b | 4 | |||
512.2.g.c | 4 | |||
512.2.g.d | 4 | |||
512.2.g.e | 8 | |||
512.2.g.f | 8 | |||
512.2.g.g | 8 | |||
512.2.g.h | 8 | |||
512.2.i | \(\chi_{512}(33, \cdot)\) | 512.2.i.a | 56 | 8 |
512.2.i.b | 56 | |||
512.2.k | \(\chi_{512}(17, \cdot)\) | 512.2.k.a | 240 | 16 |
512.2.m | \(\chi_{512}(9, \cdot)\) | None | 0 | 32 |
512.2.o | \(\chi_{512}(5, \cdot)\) | 512.2.o.a | 4032 | 64 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(512))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(512)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)