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Properties

Label 432.4.i
Level $432$
Weight $4$
Character orbit 432.i
Rep. character $\chi_{432}(145,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $34$
Newform subspaces $6$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(432, [\chi])\).

Total New Old
Modular forms 468 38 430
Cusp forms 396 34 362
Eisenstein series 72 4 68

Trace form

\( 34 q + q^{5} + q^{7} + O(q^{10}) \) \( 34 q + q^{5} + q^{7} + 65 q^{11} - q^{13} + 80 q^{17} + 4 q^{19} - 139 q^{23} - 326 q^{25} - 27 q^{29} - 89 q^{31} - 594 q^{35} - 4 q^{37} - 9 q^{41} + 127 q^{43} + 111 q^{47} - 540 q^{49} + 4 q^{53} - 246 q^{55} + 551 q^{59} - q^{61} - 17 q^{65} + q^{67} + 232 q^{71} + 824 q^{73} - 357 q^{77} + q^{79} + 883 q^{83} - 126 q^{85} - 1452 q^{89} - 2662 q^{91} - 764 q^{95} + 17 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.4.i.a 432.i 9.c $2$ $25.489$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-9\) \(-31\) $\mathrm{SU}(2)[C_{3}]$ \(q-9\zeta_{6}q^{5}+(-31+31\zeta_{6})q^{7}+(15+\cdots)q^{11}+\cdots\)
432.4.i.b 432.i 9.c $4$ $25.489$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(0\) \(0\) \(-9\) \(19\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4-4\beta _{1}-\beta _{3})q^{5}+(-1-10\beta _{1}+\cdots)q^{7}+\cdots\)
432.4.i.c 432.i 9.c $4$ $25.489$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(15\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(7\beta _{1}+\beta _{3})q^{5}+(2-5\beta _{1}-3\beta _{2}+3\beta _{3})q^{7}+\cdots\)
432.4.i.d 432.i 9.c $6$ $25.489$ 6.0.6831243.2 None \(0\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{1}+\beta _{5})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
432.4.i.e 432.i 9.c $8$ $25.489$ 8.0.5206055409.1 None \(0\) \(0\) \(5\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\beta _{6}+\beta _{7})q^{7}+\cdots\)
432.4.i.f 432.i 9.c $10$ $25.489$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{6})q^{5}+(1-\beta _{1}+\beta _{3}+\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

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