Defining parameters
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1440, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 896 | 92 | 804 |
Cusp forms | 832 | 88 | 744 |
Eisenstein series | 64 | 4 | 60 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)