Defining parameters
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(17\), \(29\), \(31\), \(83\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 408 | 100 | 308 |
Cusp forms | 360 | 92 | 268 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)