Defining parameters
Level: | \( N \) | = | \( 2116 = 2^{2} \cdot 23^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(558624\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2116))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 141526 | 81862 | 59664 |
Cusp forms | 137787 | 80454 | 57333 |
Eisenstein series | 3739 | 1408 | 2331 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2116))\)
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 |
---|---|---|---|---|
2116.2.a | \(\chi_{2116}(1, \cdot)\) | 2116.2.a.a | 1 | 1 |
2116.2.a.b | 1 | |||
2116.2.a.c | 1 | |||
2116.2.a.d | 1 | |||
2116.2.a.e | 2 | |||
2116.2.a.f | 2 | |||
2116.2.a.g | 6 | |||
2116.2.a.h | 8 | |||
2116.2.a.i | 10 | |||
2116.2.a.j | 10 | |||
2116.2.b | \(\chi_{2116}(2115, \cdot)\) | n/a | 232 | 1 |
2116.2.e | \(\chi_{2116}(177, \cdot)\) | n/a | 420 | 10 |
2116.2.h | \(\chi_{2116}(63, \cdot)\) | n/a | 2320 | 10 |
2116.2.i | \(\chi_{2116}(93, \cdot)\) | n/a | 1012 | 22 |
2116.2.l | \(\chi_{2116}(91, \cdot)\) | n/a | 6028 | 22 |
2116.2.m | \(\chi_{2116}(9, \cdot)\) | n/a | 10120 | 220 |
2116.2.n | \(\chi_{2116}(7, \cdot)\) | n/a | 60280 | 220 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2116))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2116)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)