Defining parameters
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(40, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 0 | 20 |
Cusp forms | 4 | 0 | 4 |
Eisenstein series | 16 | 0 | 16 |
Decomposition of \(S_{2}^{\mathrm{old}}(40, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(40, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)