Defining parameters
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 59 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(300\) | ||
Trace bound: | \(16\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(531, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 244 | 101 | 143 |
Cusp forms | 236 | 99 | 137 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(531, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
531.5.c.a | $3$ | $54.889$ | 3.3.1593.1 | \(\Q(\sqrt{-59}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2^{4}q^{4}+(2\beta _{1}+9\beta _{2})q^{5}+(7\beta _{1}+15\beta _{2})q^{7}+\cdots\) |
531.5.c.b | $16$ | $54.889$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(-4\) | \(-82\) | \(q+\beta _{1}q^{2}+(-12+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\) |
531.5.c.c | $40$ | $54.889$ | None | \(0\) | \(0\) | \(0\) | \(80\) | ||
531.5.c.d | $40$ | $54.889$ | None | \(0\) | \(0\) | \(0\) | \(80\) |
Decomposition of \(S_{5}^{\mathrm{old}}(531, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(531, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)