Defining parameters
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(20, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 4 | 26 |
Cusp forms | 18 | 4 | 14 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(20, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
20.5.f.a | $4$ | $2.067$ | \(\Q(i, \sqrt{241})\) | None | \(0\) | \(-10\) | \(-6\) | \(110\) | \(q+(-2+2\beta _{1}+\beta _{3})q^{3}+(-6\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(20, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)