Defining parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.p (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(80, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 14 | 46 |
Cusp forms | 36 | 10 | 26 |
Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(80, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
80.3.p.a | $2$ | $2.180$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(-6\) | \(14\) | \(q+(i-1)q^{3}+(4 i-3)q^{5}+(7 i+7)q^{7}+\cdots\) |
80.3.p.b | $2$ | $2.180$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(10\) | \(6\) | \(q+(i-1)q^{3}+5 q^{5}+(3 i+3)q^{7}+\cdots\) |
80.3.p.c | $2$ | $2.180$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q+(-2 i+2)q^{3}-5 i q^{5}+(-2 i-2)q^{7}+\cdots\) |
80.3.p.d | $4$ | $2.180$ | \(\Q(i, \sqrt{41})\) | None | \(0\) | \(2\) | \(-6\) | \(-14\) | \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(80, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)