Defining parameters
Level: | \( N \) | = | \( 261 = 3^{2} \cdot 29 \) |
Weight: | \( k \) | = | \( 12 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(60480\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(261))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 27944 | 22013 | 5931 |
Cusp forms | 27496 | 21771 | 5725 |
Eisenstein series | 448 | 242 | 206 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(261))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
261.12.a | \(\chi_{261}(1, \cdot)\) | 261.12.a.a | 11 | 1 |
261.12.a.b | 11 | |||
261.12.a.c | 12 | |||
261.12.a.d | 14 | |||
261.12.a.e | 14 | |||
261.12.a.f | 15 | |||
261.12.a.g | 26 | |||
261.12.a.h | 26 | |||
261.12.c | \(\chi_{261}(28, \cdot)\) | n/a | 136 | 1 |
261.12.e | \(\chi_{261}(88, \cdot)\) | n/a | 616 | 2 |
261.12.g | \(\chi_{261}(17, \cdot)\) | n/a | 220 | 2 |
261.12.i | \(\chi_{261}(115, \cdot)\) | n/a | 656 | 2 |
261.12.k | \(\chi_{261}(82, \cdot)\) | n/a | 822 | 6 |
261.12.l | \(\chi_{261}(41, \cdot)\) | n/a | 1312 | 4 |
261.12.o | \(\chi_{261}(64, \cdot)\) | n/a | 816 | 6 |
261.12.q | \(\chi_{261}(7, \cdot)\) | n/a | 3936 | 12 |
261.12.r | \(\chi_{261}(8, \cdot)\) | n/a | 1320 | 12 |
261.12.u | \(\chi_{261}(4, \cdot)\) | n/a | 3936 | 12 |
261.12.x | \(\chi_{261}(2, \cdot)\) | n/a | 7872 | 24 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_1(261)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)