Defining parameters
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(32, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 18 | 54 |
Cusp forms | 64 | 16 | 48 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(32, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
32.18.b.a | $16$ | $58.631$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-11529600\) | \(q-\beta _{1}q^{3}+(4\beta _{1}-\beta _{9})q^{5}+(-720600+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{18}^{\mathrm{old}}(32, [\chi])\) into lower level spaces
\( S_{18}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{18}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)