Defining parameters
Level: | \( N \) | = | \( 529 = 23^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(46552\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(529))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12012 | 11946 | 66 |
Cusp forms | 11265 | 11241 | 24 |
Eisenstein series | 747 | 705 | 42 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)
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 |
---|---|---|---|---|
529.2.a | \(\chi_{529}(1, \cdot)\) | 529.2.a.a | 2 | 1 |
529.2.a.b | 2 | |||
529.2.a.c | 2 | |||
529.2.a.d | 2 | |||
529.2.a.e | 2 | |||
529.2.a.f | 3 | |||
529.2.a.g | 4 | |||
529.2.a.h | 4 | |||
529.2.a.i | 5 | |||
529.2.a.j | 5 | |||
529.2.c | \(\chi_{529}(118, \cdot)\) | 529.2.c.a | 10 | 10 |
529.2.c.b | 10 | |||
529.2.c.c | 10 | |||
529.2.c.d | 10 | |||
529.2.c.e | 10 | |||
529.2.c.f | 10 | |||
529.2.c.g | 10 | |||
529.2.c.h | 10 | |||
529.2.c.i | 10 | |||
529.2.c.j | 20 | |||
529.2.c.k | 20 | |||
529.2.c.l | 20 | |||
529.2.c.m | 20 | |||
529.2.c.n | 20 | |||
529.2.c.o | 20 | |||
529.2.c.p | 30 | |||
529.2.c.q | 40 | |||
529.2.c.r | 40 | |||
529.2.e | \(\chi_{529}(24, \cdot)\) | 529.2.e.a | 990 | 22 |
529.2.g | \(\chi_{529}(2, \cdot)\) | 529.2.g.a | 9900 | 220 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(529))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(529)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)