Defining parameters
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(896\) | ||
Trace bound: | \(29\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\), \(19\), \(31\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 496 | 40 | 456 |
Cusp forms | 400 | 40 | 360 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)