Defining parameters
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 468 | 114 | 354 |
Cusp forms | 396 | 102 | 294 |
Eisenstein series | 72 | 12 | 60 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
432.2.u.a | $6$ | $3.450$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(0\) | \(-3\) | \(-3\) | \(q+(-2\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\) |
432.2.u.b | $12$ | $3.450$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(-3\) | \(3\) | \(q+(\beta _{3}-\beta _{4}-\beta _{11})q^{3}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\) |
432.2.u.c | $12$ | $3.450$ | 12.0.\(\cdots\).1 | None | \(0\) | \(6\) | \(-3\) | \(6\) | \(q+(-\beta _{2}+\beta _{6}+\beta _{7}-\beta _{9})q^{3}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\) |
432.2.u.d | $18$ | $3.450$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(0\) | \(0\) | \(3\) | \(0\) | \(q-\beta _{12}q^{3}+(-1+\beta _{1}-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\) |
432.2.u.e | $24$ | $3.450$ | None | \(0\) | \(0\) | \(0\) | \(3\) | ||
432.2.u.f | $30$ | $3.450$ | None | \(0\) | \(0\) | \(0\) | \(-3\) |
Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)