Defining parameters
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.i (of order \(29\) and degree \(28\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 59 \) |
Character field: | \(\Q(\zeta_{29})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(531, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1792 | 728 | 1064 |
Cusp forms | 1568 | 672 | 896 |
Eisenstein series | 224 | 56 | 168 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(531, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
531.2.i.a | $112$ | $4.240$ | None | \(26\) | \(0\) | \(25\) | \(-23\) | ||
531.2.i.b | $140$ | $4.240$ | None | \(-1\) | \(0\) | \(-2\) | \(-2\) | ||
531.2.i.c | $140$ | $4.240$ | None | \(1\) | \(0\) | \(2\) | \(-2\) | ||
531.2.i.d | $280$ | $4.240$ | None | \(0\) | \(0\) | \(0\) | \(-4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(531, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(531, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)