Defining parameters
Level: | \( N \) | = | \( 841 = 29^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 51 \) | ||
Sturm bound: | \(117740\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(841))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30037 | 29939 | 98 |
Cusp forms | 28834 | 28790 | 44 |
Eisenstein series | 1203 | 1149 | 54 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)
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 |
---|---|---|---|---|
841.2.a | \(\chi_{841}(1, \cdot)\) | 841.2.a.a | 2 | 1 |
841.2.a.b | 2 | |||
841.2.a.c | 2 | |||
841.2.a.d | 2 | |||
841.2.a.e | 3 | |||
841.2.a.f | 3 | |||
841.2.a.g | 6 | |||
841.2.a.h | 6 | |||
841.2.a.i | 8 | |||
841.2.a.j | 8 | |||
841.2.a.k | 12 | |||
841.2.b | \(\chi_{841}(840, \cdot)\) | 841.2.b.a | 4 | 1 |
841.2.b.b | 4 | |||
841.2.b.c | 6 | |||
841.2.b.d | 12 | |||
841.2.b.e | 12 | |||
841.2.b.f | 16 | |||
841.2.d | \(\chi_{841}(190, \cdot)\) | 841.2.d.a | 6 | 6 |
841.2.d.b | 6 | |||
841.2.d.c | 6 | |||
841.2.d.d | 6 | |||
841.2.d.e | 6 | |||
841.2.d.f | 12 | |||
841.2.d.g | 12 | |||
841.2.d.h | 12 | |||
841.2.d.i | 12 | |||
841.2.d.j | 12 | |||
841.2.d.k | 24 | |||
841.2.d.l | 24 | |||
841.2.d.m | 24 | |||
841.2.d.n | 36 | |||
841.2.d.o | 36 | |||
841.2.d.p | 48 | |||
841.2.d.q | 48 | |||
841.2.e | \(\chi_{841}(63, \cdot)\) | 841.2.e.a | 12 | 6 |
841.2.e.b | 12 | |||
841.2.e.c | 12 | |||
841.2.e.d | 12 | |||
841.2.e.e | 12 | |||
841.2.e.f | 12 | |||
841.2.e.g | 12 | |||
841.2.e.h | 12 | |||
841.2.e.i | 12 | |||
841.2.e.j | 24 | |||
841.2.e.k | 24 | |||
841.2.e.l | 72 | |||
841.2.e.m | 96 | |||
841.2.g | \(\chi_{841}(30, \cdot)\) | 841.2.g.a | 1988 | 28 |
841.2.h | \(\chi_{841}(28, \cdot)\) | 841.2.h.a | 2016 | 28 |
841.2.j | \(\chi_{841}(7, \cdot)\) | 841.2.j.a | 11928 | 168 |
841.2.k | \(\chi_{841}(4, \cdot)\) | 841.2.k.a | 12096 | 168 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(841))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(841)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)