Defining parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.n (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 6 | 30 |
Cusp forms | 12 | 6 | 6 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(80, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
80.2.n.a | $2$ | $0.639$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(2+i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots\) |
80.2.n.b | $4$ | $0.639$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}+(-1-2\zeta_{12})q^{5}+\zeta_{12}^{3}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(80, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)