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Properties

Label 432.6.i
Level $432$
Weight $6$
Character orbit 432.i
Rep. character $\chi_{432}(145,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $58$
Newform subspaces $6$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(432\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(432, [\chi])\).

Total New Old
Modular forms 756 62 694
Cusp forms 684 58 626
Eisenstein series 72 4 68

Trace form

\( 58 q + q^{5} + q^{7} + O(q^{10}) \) \( 58 q + q^{5} + q^{7} - 727 q^{11} - q^{13} - 1000 q^{17} + 4 q^{19} + 3173 q^{23} - 15626 q^{25} + 3981 q^{29} - 1625 q^{31} + 35646 q^{35} - 4 q^{37} - 2901 q^{41} - 13865 q^{43} + 37935 q^{47} - 55224 q^{49} + 4 q^{53} - 6246 q^{55} - 55033 q^{59} - q^{61} + 5743 q^{65} + q^{67} - 23672 q^{71} - 53632 q^{73} - 24885 q^{77} + q^{79} - 41693 q^{83} - 3126 q^{85} - 207948 q^{89} - 80758 q^{91} - 61748 q^{95} - 58147 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.6.i.a 432.i 9.c $4$ $69.286$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(54\) \(-74\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3^{3}\beta _{1}+2\beta _{2})q^{5}+(-37+37\beta _{1}+\cdots)q^{7}+\cdots\)
432.6.i.b 432.i 9.c $6$ $69.286$ 6.0.\(\cdots\).3 None \(0\) \(0\) \(54\) \(132\) $\mathrm{SU}(2)[C_{3}]$ \(q+(18-18\beta _{1}-\beta _{5})q^{5}+(44\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
432.6.i.c 432.i 9.c $8$ $69.286$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-78\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-19\beta _{1}+\beta _{2}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
432.6.i.d 432.i 9.c $10$ $69.286$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(21\) \(-29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{1}+\beta _{7})q^{5}+(-6\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
432.6.i.e 432.i 9.c $14$ $69.286$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(-25\) \(-93\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\beta _{1}-\beta _{3}+\beta _{6})q^{5}+(-13\beta _{1}+\cdots)q^{7}+\cdots\)
432.6.i.f 432.i 9.c $16$ $69.286$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-25\) \(93\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3\beta _{8}-\beta _{10})q^{5}+(12-\beta _{2}-12\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)