Defining parameters
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(135\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(50, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 134 | 26 | 108 |
Cusp forms | 122 | 26 | 96 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(50, [\chi])\) into newform subspaces
Decomposition of \(S_{18}^{\mathrm{old}}(50, [\chi])\) into lower level spaces
\( S_{18}^{\mathrm{old}}(50, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)