Defining parameters
Level: | \( N \) | = | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 49 \) | ||
Sturm bound: | \(29040\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(363))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10000 | 7282 | 2718 |
Cusp forms | 9360 | 7000 | 2360 |
Eisenstein series | 640 | 282 | 358 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(363))\)
We only show spaces with odd 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 |
---|---|---|---|---|
363.3.b | \(\chi_{363}(122, \cdot)\) | 363.3.b.a | 1 | 1 |
363.3.b.b | 1 | |||
363.3.b.c | 2 | |||
363.3.b.d | 2 | |||
363.3.b.e | 2 | |||
363.3.b.f | 4 | |||
363.3.b.g | 4 | |||
363.3.b.h | 4 | |||
363.3.b.i | 4 | |||
363.3.b.j | 6 | |||
363.3.b.k | 6 | |||
363.3.b.l | 8 | |||
363.3.b.m | 8 | |||
363.3.b.n | 12 | |||
363.3.c | \(\chi_{363}(241, \cdot)\) | 363.3.c.a | 4 | 1 |
363.3.c.b | 4 | |||
363.3.c.c | 4 | |||
363.3.c.d | 8 | |||
363.3.c.e | 16 | |||
363.3.g | \(\chi_{363}(40, \cdot)\) | 363.3.g.a | 16 | 4 |
363.3.g.b | 16 | |||
363.3.g.c | 16 | |||
363.3.g.d | 16 | |||
363.3.g.e | 16 | |||
363.3.g.f | 16 | |||
363.3.g.g | 16 | |||
363.3.g.h | 32 | |||
363.3.h | \(\chi_{363}(245, \cdot)\) | 363.3.h.a | 4 | 4 |
363.3.h.b | 4 | |||
363.3.h.c | 8 | |||
363.3.h.d | 8 | |||
363.3.h.e | 8 | |||
363.3.h.f | 8 | |||
363.3.h.g | 8 | |||
363.3.h.h | 8 | |||
363.3.h.i | 8 | |||
363.3.h.j | 16 | |||
363.3.h.k | 16 | |||
363.3.h.l | 16 | |||
363.3.h.m | 16 | |||
363.3.h.n | 16 | |||
363.3.h.o | 16 | |||
363.3.h.p | 24 | |||
363.3.h.q | 24 | |||
363.3.h.r | 48 | |||
363.3.k | \(\chi_{363}(10, \cdot)\) | 363.3.k.a | 440 | 10 |
363.3.l | \(\chi_{363}(23, \cdot)\) | 363.3.l.a | 860 | 10 |
363.3.n | \(\chi_{363}(5, \cdot)\) | 363.3.n.a | 3440 | 40 |
363.3.o | \(\chi_{363}(7, \cdot)\) | 363.3.o.a | 1760 | 40 |
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(363)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)