Defining parameters
Level: | \( N \) | = | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 45 \) | ||
Sturm bound: | \(19360\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(363))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5160 | 3711 | 1449 |
Cusp forms | 4521 | 3431 | 1090 |
Eisenstein series | 639 | 280 | 359 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)
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 |
---|---|---|---|---|
363.2.a | \(\chi_{363}(1, \cdot)\) | 363.2.a.a | 1 | 1 |
363.2.a.b | 1 | |||
363.2.a.c | 1 | |||
363.2.a.d | 2 | |||
363.2.a.e | 2 | |||
363.2.a.f | 2 | |||
363.2.a.g | 2 | |||
363.2.a.h | 2 | |||
363.2.a.i | 2 | |||
363.2.a.j | 4 | |||
363.2.d | \(\chi_{363}(362, \cdot)\) | 363.2.d.a | 2 | 1 |
363.2.d.b | 2 | |||
363.2.d.c | 4 | |||
363.2.d.d | 4 | |||
363.2.d.e | 8 | |||
363.2.d.f | 8 | |||
363.2.e | \(\chi_{363}(124, \cdot)\) | 363.2.e.a | 4 | 4 |
363.2.e.b | 4 | |||
363.2.e.c | 4 | |||
363.2.e.d | 4 | |||
363.2.e.e | 4 | |||
363.2.e.f | 4 | |||
363.2.e.g | 4 | |||
363.2.e.h | 4 | |||
363.2.e.i | 4 | |||
363.2.e.j | 4 | |||
363.2.e.k | 4 | |||
363.2.e.l | 4 | |||
363.2.e.m | 8 | |||
363.2.e.n | 16 | |||
363.2.f | \(\chi_{363}(161, \cdot)\) | 363.2.f.a | 8 | 4 |
363.2.f.b | 8 | |||
363.2.f.c | 8 | |||
363.2.f.d | 8 | |||
363.2.f.e | 8 | |||
363.2.f.f | 8 | |||
363.2.f.g | 16 | |||
363.2.f.h | 16 | |||
363.2.f.i | 32 | |||
363.2.i | \(\chi_{363}(34, \cdot)\) | 363.2.i.a | 110 | 10 |
363.2.i.b | 110 | |||
363.2.j | \(\chi_{363}(32, \cdot)\) | 363.2.j.a | 420 | 10 |
363.2.m | \(\chi_{363}(4, \cdot)\) | 363.2.m.a | 440 | 40 |
363.2.m.b | 440 | |||
363.2.p | \(\chi_{363}(2, \cdot)\) | 363.2.p.a | 1680 | 40 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(363)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)