Defining parameters
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.n (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(160, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 12 | 52 |
Cusp forms | 32 | 12 | 20 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(160, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
160.2.n.a | $2$ | $1.278$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-4\) | \(-4\) | \(-4\) | \(q+(-2-2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots\) |
160.2.n.b | $2$ | $1.278$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(2\) | \(-2\) | \(q+(-1-i)q^{3}+(1-2i)q^{5}+(-1+i)q^{7}+\cdots\) |
160.2.n.c | $2$ | $1.278$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(2\) | \(6\) | \(q+(-1-i)q^{3}+(1+2i)q^{5}+(3-3i)q^{7}+\cdots\) |
160.2.n.d | $2$ | $1.278$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(2\) | \(-6\) | \(q+(1+i)q^{3}+(1+2i)q^{5}+(-3+3i)q^{7}+\cdots\) |
160.2.n.e | $2$ | $1.278$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(2\) | \(2\) | \(q+(1+i)q^{3}+(1-2i)q^{5}+(1-i)q^{7}+\cdots\) |
160.2.n.f | $2$ | $1.278$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(4\) | \(-4\) | \(4\) | \(q+(2+2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(160, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)