Defining parameters
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.p (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(160, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 24 | 88 |
Cusp forms | 80 | 24 | 56 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(160, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
160.3.p.a | $2$ | $4.360$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(-8\) | \(0\) | \(q+(-4+3i)q^{5}+9iq^{9}+(-17+17i)q^{13}+\cdots\) |
160.3.p.b | $2$ | $4.360$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(8\) | \(0\) | \(q+(4+3i)q^{5}+9iq^{9}+(7-7i)q^{13}+\cdots\) |
160.3.p.c | $4$ | $4.360$ | \(\Q(i, \sqrt{15})\) | None | \(0\) | \(0\) | \(-20\) | \(0\) | \(q-\beta _{2}q^{3}-5q^{5}+\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots\) |
160.3.p.d | $4$ | $4.360$ | \(\Q(i, \sqrt{7})\) | None | \(0\) | \(0\) | \(12\) | \(0\) | \(q-\beta _{2}q^{3}+(3+4\beta _{1})q^{5}-3\beta _{3}q^{7}+5\beta _{1}q^{9}+\cdots\) |
160.3.p.e | $6$ | $4.360$ | 6.0.3534400.1 | None | \(0\) | \(0\) | \(4\) | \(-8\) | \(q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots\) |
160.3.p.f | $6$ | $4.360$ | 6.0.3534400.1 | None | \(0\) | \(0\) | \(4\) | \(8\) | \(q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(160, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)