Defining parameters
Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 704.w (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 88 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(704, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 432 | 96 | 336 |
Cusp forms | 336 | 96 | 240 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(704, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
704.2.w.a | $16$ | $5.621$ | \(\Q(\zeta_{40})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{40}^{4}-\zeta_{40}^{6}+\zeta_{40}^{7}+\zeta_{40}^{8}+\cdots)q^{3}+\cdots\) |
704.2.w.b | $16$ | $5.621$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(2\beta _{2}-\beta _{4}+\beta _{5}+2\beta _{9})q^{3}+(\beta _{6}+\beta _{11}+\cdots)q^{5}+\cdots\) |
704.2.w.c | $64$ | $5.621$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(704, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)