Defining parameters
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(40\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(32, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 10 | 30 |
Cusp forms | 32 | 8 | 24 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(32, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
32.10.b.a | $8$ | $16.481$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-4800\) | \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-600-\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(32, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(32, [\chi]) \cong \)