Defining parameters
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(448\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1568, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 40 | 216 |
Cusp forms | 192 | 40 | 152 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1568.2.f.a | $8$ | $12.521$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{16}^{7}q^{3}+(-\zeta_{16}^{2}+\zeta_{16}^{4})q^{5}+\cdots\) |
1568.2.f.b | $16$ | $12.521$ | 16.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{13}q^{5}+(1-\beta _{2})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\) |
1568.2.f.c | $16$ | $12.521$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{12}q^{3}+(\beta _{5}+\beta _{7})q^{5}+(2+\beta _{3})q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \)