Defining parameters
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.g (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(70, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 8 | 24 |
Cusp forms | 16 | 8 | 8 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(70, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
70.2.g.a | $8$ | $0.559$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\zeta_{16}^{6}q^{2}+(\zeta_{16}-\zeta_{16}^{3})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(70, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)