Defining parameters
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cj (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 56 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 84 | 124 |
Cusp forms | 176 | 76 | 100 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
504.2.cj.a | $8$ | $4.024$ | 8.0.12960000.1 | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+(\beta _{4}+\beta _{5})q^{2}+\beta _{6}q^{4}+(\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\) |
504.2.cj.b | $8$ | $4.024$ | \(\Q(\zeta_{24})\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\zeta_{24}^{5}q^{2}+2\zeta_{24}q^{4}+(-\zeta_{24}^{2}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\) |
504.2.cj.c | $12$ | $4.024$ | 12.0.\(\cdots\).1 | None | \(2\) | \(0\) | \(0\) | \(-4\) | \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{3}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\) |
504.2.cj.d | $16$ | $4.024$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{13}+\cdots)q^{4}+\cdots\) |
504.2.cj.e | $32$ | $4.024$ | None | \(-2\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)