Defining parameters
Level: | \( N \) | = | \( 169 = 13^{2} \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(23660\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(169))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10761 | 10624 | 137 |
Cusp forms | 10533 | 10419 | 114 |
Eisenstein series | 228 | 205 | 23 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(169))\)
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 |
---|---|---|---|---|
169.10.a | \(\chi_{169}(1, \cdot)\) | 169.10.a.a | 4 | 1 |
169.10.a.b | 5 | |||
169.10.a.c | 9 | |||
169.10.a.d | 9 | |||
169.10.a.e | 10 | |||
169.10.a.f | 20 | |||
169.10.a.g | 27 | |||
169.10.a.h | 27 | |||
169.10.b | \(\chi_{169}(168, \cdot)\) | n/a | 110 | 1 |
169.10.c | \(\chi_{169}(22, \cdot)\) | n/a | 222 | 2 |
169.10.e | \(\chi_{169}(23, \cdot)\) | n/a | 220 | 2 |
169.10.g | \(\chi_{169}(14, \cdot)\) | n/a | 1620 | 12 |
169.10.h | \(\chi_{169}(12, \cdot)\) | n/a | 1632 | 12 |
169.10.i | \(\chi_{169}(3, \cdot)\) | n/a | 3240 | 24 |
169.10.k | \(\chi_{169}(4, \cdot)\) | n/a | 3264 | 24 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 1}\)