Defining parameters
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(64, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 14 | 42 |
Cusp forms | 40 | 10 | 30 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(64, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
64.4.e.a | $10$ | $3.776$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(0\) | \(2\) | \(-2\) | \(0\) | \(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(64, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(64, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)