Defining parameters
| Level: | \( N \) | \(=\) | \( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1740.by (of order \(14\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 145 \) |
| Character field: | \(\Q(\zeta_{14})\) | ||
| Sturm bound: | \(720\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1740, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2232 | 192 | 2040 |
| Cusp forms | 2088 | 192 | 1896 |
| Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1740, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(1740, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(870, [\chi])\)\(^{\oplus 2}\)