Defining parameters
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.x (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 936 | 96 | 840 |
Cusp forms | 792 | 96 | 696 |
Eisenstein series | 144 | 0 | 144 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)