Defining parameters
Level: | \( N \) | \(=\) | \( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5328.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 18 \) | ||
Sturm bound: | \(1824\) | ||
Trace bound: | \(41\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5328, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 936 | 96 | 840 |
Cusp forms | 888 | 94 | 794 |
Eisenstein series | 48 | 2 | 46 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(5328, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(5328, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5328, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 4}\)