Defining parameters
Level: | \( N \) | \(=\) | \( 999 = 3^{3} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 999.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(228\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(999, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 50 | 70 |
Cusp forms | 108 | 50 | 58 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(999, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(999, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(999, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)