Defining parameters
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(567, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 312 | 96 | 216 |
Cusp forms | 264 | 96 | 168 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(567, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
567.3.r.a | $8$ | $15.450$ | 8.0.\(\cdots\).5 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}-2\beta _{5}q^{5}-\beta _{6}q^{7}+\cdots\) |
567.3.r.b | $8$ | $15.450$ | 8.0.\(\cdots\).5 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{6})q^{4}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots\) |
567.3.r.c | $8$ | $15.450$ | 8.0.\(\cdots\).8 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}+(3-2\beta _{1}+3\beta _{3})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\) |
567.3.r.d | $8$ | $15.450$ | 8.0.\(\cdots\).53 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{1}-\beta _{3})q^{2}+(6+6\beta _{2}-\beta _{6})q^{4}+\cdots\) |
567.3.r.e | $16$ | $15.450$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{8}q^{2}+(1-\beta _{2}+\beta _{5}-\beta _{7}+\beta _{15})q^{4}+\cdots\) |
567.3.r.f | $48$ | $15.450$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(567, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)