Defining parameters
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.k (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(60, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 108 | 8 | 100 |
Cusp forms | 84 | 8 | 76 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(60, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
60.5.k.a | $8$ | $6.202$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(12\) | \(-140\) | \(q+\beta _{2}q^{3}+(2+2\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(60, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)