Defining parameters
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(32, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 6 | 22 |
Cusp forms | 20 | 6 | 14 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(32, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
32.7.c.a | $2$ | $7.362$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(100\) | \(0\) | \(q+iq^{3}+50q^{5}+46iq^{7}+713q^{9}+\cdots\) |
32.7.c.b | $4$ | $7.362$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(-56\) | \(0\) | \(q-\beta _{1}q^{3}+(-14-\beta _{3})q^{5}+(2\beta _{1}-5\beta _{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(32, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)