Defining parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(80, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 10 | 32 |
Cusp forms | 30 | 8 | 22 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(80, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
80.4.c.a | $2$ | $4.720$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-10\) | \(0\) | \(q+iq^{3}+(-5-5i)q^{5}-13iq^{7}+23q^{9}+\cdots\) |
80.4.c.b | $2$ | $4.720$ | \(\Q(\sqrt{-19}) \) | None | \(0\) | \(0\) | \(14\) | \(0\) | \(q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\) |
80.4.c.c | $4$ | $4.720$ | \(\Q(i, \sqrt{6})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(80, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(80, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)