Defining parameters
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.q (of order \(39\) and degree \(24\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 169 \) |
Character field: | \(\Q(\zeta_{39})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(121\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(507, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1512 | 744 | 768 |
Cusp forms | 1416 | 744 | 672 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(507, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
507.2.q.a | $360$ | $4.048$ | None | \(1\) | \(-15\) | \(2\) | \(2\) | ||
507.2.q.b | $384$ | $4.048$ | None | \(1\) | \(16\) | \(6\) | \(-3\) |
Decomposition of \(S_{2}^{\mathrm{old}}(507, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(507, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)