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Properties

Label 432.2.u
Level $432$
Weight $2$
Character orbit 432.u
Rep. character $\chi_{432}(49,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $102$
Newform subspaces $6$
Sturm bound $144$
Trace bound $3$

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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

\( 102 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + O(q^{10}) \) \( 102 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} + 6 q^{15} - 3 q^{17} + 3 q^{19} - 6 q^{21} + 6 q^{23} - 6 q^{25} + 24 q^{27} - 18 q^{29} + 6 q^{31} + 39 q^{35} - 3 q^{37} + 42 q^{39} + 6 q^{43} - 18 q^{45} + 24 q^{47} - 6 q^{49} - 3 q^{51} - 12 q^{53} + 12 q^{55} - 3 q^{57} - 12 q^{59} - 6 q^{61} - 24 q^{63} - 30 q^{65} + 6 q^{67} - 30 q^{69} - 39 q^{71} - 3 q^{73} - 36 q^{75} - 30 q^{77} + 6 q^{79} - 30 q^{81} - 24 q^{83} + 9 q^{85} - 12 q^{87} + 3 q^{89} + 3 q^{91} - 6 q^{93} - 117 q^{95} - 24 q^{97} - 102 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.2.u.a 432.u 27.e $6$ $3.450$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-2\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
432.2.u.b 432.u 27.e $12$ $3.450$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{3}-\beta _{4}-\beta _{11})q^{3}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
432.2.u.c 432.u 27.e $12$ $3.450$ 12.0.\(\cdots\).1 None \(0\) \(6\) \(-3\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{2}+\beta _{6}+\beta _{7}-\beta _{9})q^{3}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
432.2.u.d 432.u 27.e $18$ $3.450$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{12}q^{3}+(-1+\beta _{1}-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
432.2.u.e 432.u 27.e $24$ $3.450$ None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$
432.2.u.f 432.u 27.e $30$ $3.450$ None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)