Defining parameters
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3920, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 720 | 80 | 640 |
Cusp forms | 624 | 80 | 544 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3920.2.k.a | $8$ | $31.301$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(-8\) | \(0\) | \(0\) | \(q+(-1+\zeta_{16}^{5}+\zeta_{16}^{6})q^{3}+\zeta_{16}q^{5}+\cdots\) |
3920.2.k.b | $8$ | $31.301$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{5}q^{3}+\zeta_{24}q^{5}+(-1-\zeta_{24}^{3}+\cdots)q^{9}+\cdots\) |
3920.2.k.c | $8$ | $31.301$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(8\) | \(0\) | \(0\) | \(q+(1-\zeta_{16}^{5}-\zeta_{16}^{6})q^{3}+\zeta_{16}q^{5}+\cdots\) |
3920.2.k.d | $12$ | $31.301$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2+\beta _{2}+\beta _{4})q^{9}+\cdots\) |
3920.2.k.e | $12$ | $31.301$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}+\beta _{6}q^{5}+(2+\beta _{2}+\beta _{4})q^{9}+\cdots\) |
3920.2.k.f | $32$ | $31.301$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \)