Defining parameters
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(3\) | ||
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 | 36 | 172 |
Cusp forms | 176 | 36 | 140 |
Eisenstein series | 32 | 0 | 32 |
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.r.a | $2$ | $4.024$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(1\) | \(-1\) | \(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\) |
504.2.r.b | $2$ | $4.024$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(3\) | \(-2\) | \(-1\) | \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots\) |
504.2.r.c | $6$ | $4.024$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(0\) | \(3\) | \(-3\) | \(q+(-\beta_{5}-\beta_{2})q^{3}+(-\beta_{3}+\beta_{2}-\beta_1+1)q^{5}+\cdots\) |
504.2.r.d | $8$ | $4.024$ | 8.0.508277025.1 | None | \(0\) | \(-4\) | \(4\) | \(-4\) | \(q+(-\beta _{4}-\beta _{6})q^{3}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\) |
504.2.r.e | $8$ | $4.024$ | 8.0.2091141441.1 | None | \(0\) | \(-1\) | \(-3\) | \(4\) | \(q+\beta _{4}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\) |
504.2.r.f | $10$ | $4.024$ | 10.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(-3\) | \(5\) | \(q+\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)