Defining parameters
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 85 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(170, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 8 | 24 |
Cusp forms | 24 | 8 | 16 |
Eisenstein series | 8 | 0 | 8 |
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.d.a | $2$ | $1.357$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(-4\) | \(-4\) | \(q+iq^{2}-q^{3}-q^{4}+(-2+i)q^{5}-iq^{6}+\cdots\) |
170.2.d.b | $2$ | $1.357$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(4\) | \(4\) | \(q+iq^{2}+q^{3}-q^{4}+(2-i)q^{5}+iq^{6}+\cdots\) |
170.2.d.c | $4$ | $1.357$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}-q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(170, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)