Defining parameters
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4032, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 816 | 82 | 734 |
Cusp forms | 720 | 78 | 642 |
Eisenstein series | 96 | 4 | 92 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(4032, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)