Defining parameters
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{20}(64, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 158 | 38 | 120 |
Cusp forms | 146 | 38 | 108 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{20}^{\mathrm{new}}(64, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
64.20.b.a | $2$ | $146.443$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+26107iq^{3}-1564040329q^{9}+\cdots\) |
64.20.b.b | $12$ | $146.443$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(3^{3}\beta _{6}-\beta _{7})q^{3}-\beta _{2}q^{5}-\beta _{8}q^{7}+\cdots\) |
64.20.b.c | $24$ | $146.443$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{20}^{\mathrm{old}}(64, [\chi])\) into lower level spaces
\( S_{20}^{\mathrm{old}}(64, [\chi]) \cong \)