Defining parameters
| Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3750.g (of order \(5\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
| Character field: | \(\Q(\zeta_{5})\) | ||
| Sturm bound: | \(1500\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3750, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3240 | 320 | 2920 |
| Cusp forms | 2760 | 320 | 2440 |
| Eisenstein series | 480 | 0 | 480 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3750, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(3750, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3750, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1250, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1875, [\chi])\)\(^{\oplus 2}\)