Defining parameters
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.l (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(1728\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(2880, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1200 | 64 | 1136 |
Cusp forms | 1104 | 64 | 1040 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)