Defining parameters
Level: | \( N \) | = | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(16896\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(276))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6556 | 2798 | 3758 |
Cusp forms | 6116 | 2718 | 3398 |
Eisenstein series | 440 | 80 | 360 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(276))\)
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 |
---|---|---|---|---|
276.4.a | \(\chi_{276}(1, \cdot)\) | 276.4.a.a | 1 | 1 |
276.4.a.b | 1 | |||
276.4.a.c | 2 | |||
276.4.a.d | 2 | |||
276.4.a.e | 4 | |||
276.4.c | \(\chi_{276}(47, \cdot)\) | n/a | 132 | 1 |
276.4.e | \(\chi_{276}(91, \cdot)\) | 276.4.e.a | 72 | 1 |
276.4.g | \(\chi_{276}(137, \cdot)\) | 276.4.g.a | 24 | 1 |
276.4.i | \(\chi_{276}(13, \cdot)\) | n/a | 120 | 10 |
276.4.k | \(\chi_{276}(5, \cdot)\) | n/a | 240 | 10 |
276.4.m | \(\chi_{276}(7, \cdot)\) | n/a | 720 | 10 |
276.4.o | \(\chi_{276}(35, \cdot)\) | n/a | 1400 | 10 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(276))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(276)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)