Defining parameters
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.j (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(486\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(810, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 696 | 96 | 600 |
Cusp forms | 600 | 96 | 504 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(810, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(810, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)