Defining parameters
Level: | \( N \) | \(=\) | \( 3136 = 2^{6} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3136.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(896\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(17\), \(31\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 496 | 82 | 414 |
Cusp forms | 400 | 82 | 318 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)