Defining parameters
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.g (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 85 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(170, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 16 | 48 |
Cusp forms | 48 | 16 | 32 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(170, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
170.2.g.a | $2$ | $1.357$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(2\) | \(2\) | \(-6\) | \(q-q^{2}+(1-i)q^{3}+q^{4}+(1-2i)q^{5}+\cdots\) |
170.2.g.b | $2$ | $1.357$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(2\) | \(2\) | \(2\) | \(q-q^{2}+(1-i)q^{3}+q^{4}+(1+2i)q^{5}+\cdots\) |
170.2.g.c | $2$ | $1.357$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(-2\) | \(-4\) | \(6\) | \(q+q^{2}+(-1+i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\) |
170.2.g.d | $2$ | $1.357$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(-2\) | \(4\) | \(-2\) | \(q+q^{2}+(-1+i)q^{3}+q^{4}+(2+i)q^{5}+\cdots\) |
170.2.g.e | $4$ | $1.357$ | \(\Q(\zeta_{8})\) | None | \(-4\) | \(-4\) | \(0\) | \(4\) | \(q-q^{2}+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+\cdots\) |
170.2.g.f | $4$ | $1.357$ | \(\Q(\zeta_{8})\) | None | \(4\) | \(4\) | \(0\) | \(-4\) | \(q+q^{2}+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+(\zeta_{8}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(170, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)