Defining parameters
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 180 | 14 | 166 |
Cusp forms | 108 | 10 | 98 |
Eisenstein series | 72 | 4 | 68 |
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.i.a | $2$ | $3.450$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(-1\) | \(-3\) | \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\) |
432.2.i.b | $2$ | $3.450$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+(2-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots\) |
432.2.i.c | $2$ | $3.450$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(3\) | \(-1\) | \(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\) |
432.2.i.d | $4$ | $3.450$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(0\) | \(0\) | \(-1\) | \(3\) | \(q+(-\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)