Defining parameters
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
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: | \(192\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{24}(64, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 190 | 46 | 144 |
Cusp forms | 178 | 46 | 132 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{24}^{\mathrm{new}}(64, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
64.24.b.a | $2$ | $214.531$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+306773iq^{3}-282295515289q^{9}+\cdots\) |
64.24.b.b | $12$ | $214.531$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(91\beta _{2}-\beta _{5})q^{3}+\beta _{1}q^{5}+\beta _{9}q^{7}+\cdots\) |
64.24.b.c | $32$ | $214.531$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{24}^{\mathrm{old}}(64, [\chi])\) into lower level spaces
\( S_{24}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{24}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)