Defining parameters
Level: | \( N \) | = | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 28 \) | ||
Sturm bound: | \(12672\) | ||
Trace bound: | \(6\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(322))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3432 | 1011 | 2421 |
Cusp forms | 2905 | 1011 | 1894 |
Eisenstein series | 527 | 0 | 527 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)
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 |
---|---|---|---|---|
322.2.a | \(\chi_{322}(1, \cdot)\) | 322.2.a.a | 1 | 1 |
322.2.a.b | 1 | |||
322.2.a.c | 1 | |||
322.2.a.d | 1 | |||
322.2.a.e | 2 | |||
322.2.a.f | 2 | |||
322.2.a.g | 3 | |||
322.2.c | \(\chi_{322}(321, \cdot)\) | 322.2.c.a | 4 | 1 |
322.2.c.b | 4 | |||
322.2.c.c | 4 | |||
322.2.c.d | 4 | |||
322.2.e | \(\chi_{322}(93, \cdot)\) | 322.2.e.a | 8 | 2 |
322.2.e.b | 8 | |||
322.2.e.c | 8 | |||
322.2.e.d | 8 | |||
322.2.g | \(\chi_{322}(45, \cdot)\) | 322.2.g.a | 16 | 2 |
322.2.g.b | 16 | |||
322.2.i | \(\chi_{322}(29, \cdot)\) | 322.2.i.a | 10 | 10 |
322.2.i.b | 10 | |||
322.2.i.c | 20 | |||
322.2.i.d | 40 | |||
322.2.i.e | 40 | |||
322.2.k | \(\chi_{322}(83, \cdot)\) | 322.2.k.a | 80 | 10 |
322.2.k.b | 80 | |||
322.2.m | \(\chi_{322}(9, \cdot)\) | 322.2.m.a | 160 | 20 |
322.2.m.b | 160 | |||
322.2.o | \(\chi_{322}(5, \cdot)\) | 322.2.o.a | 160 | 20 |
322.2.o.b | 160 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(322))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(322)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)