Defining parameters
Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 704.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 88 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
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 | 108 | 24 | 84 |
Cusp forms | 84 | 24 | 60 |
Eisenstein series | 24 | 0 | 24 |
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.g.a | $4$ | $5.621$ | \(\Q(i, \sqrt{11})\) | \(\Q(\sqrt{-22}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-3q^{9}+\beta _{3}q^{11}-\beta _{2}q^{13}+2\beta _{3}q^{19}+\cdots\) |
704.2.g.b | $4$ | $5.621$ | \(\Q(i, \sqrt{11})\) | \(\Q(\sqrt{-11}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+8q^{9}+\beta _{2}q^{11}+\cdots\) |
704.2.g.c | $8$ | $5.621$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{4}q^{3}+\zeta_{24}^{2}q^{5}+\zeta_{24}^{5}q^{7}+\cdots\) |
704.2.g.d | $8$ | $5.621$ | 8.0.303595776.1 | \(\Q(\sqrt{-11}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{3}+\beta _{5})q^{3}+\beta _{1}q^{5}+(1-\beta _{4})q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(704, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)