Defining parameters
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(60, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 6 | 48 |
Cusp forms | 42 | 6 | 36 |
Eisenstein series | 12 | 0 | 12 |
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.g.a | $2$ | $6.202$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(12\) | \(0\) | \(148\) | \(q+(6+3\beta )q^{3}-5\beta q^{5}+74q^{7}+(-9+\cdots)q^{9}+\cdots\) |
60.5.g.b | $4$ | $6.202$ | \(\Q(\sqrt{-5}, \sqrt{34})\) | None | \(0\) | \(-20\) | \(0\) | \(-40\) | \(q+(-5+\beta _{1})q^{3}-\beta _{3}q^{5}+(-10-\beta _{1}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(60, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(60, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)