Defining parameters
Level: | \( N \) | \(=\) | \( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1650.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 165 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(7\), \(23\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1650, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 72 | 312 |
Cusp forms | 336 | 72 | 264 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1650, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)