Defining parameters
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(29\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 306 | 24 | 282 |
Cusp forms | 234 | 24 | 210 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)