Defining parameters
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 16 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(80, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 16 | 12 |
Cusp forms | 20 | 16 | 4 |
Eisenstein series | 8 | 0 | 8 |
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.l.a | $16$ | $0.639$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(80, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(80, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)