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Properties

Label 432.3.bc
Level $432$
Weight $3$
Character orbit 432.bc
Rep. character $\chi_{432}(65,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $210$
Newform subspaces $4$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 432.bc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 4 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(432, [\chi])\).

Total New Old
Modular forms 900 222 678
Cusp forms 828 210 618
Eisenstein series 72 12 60

Trace form

\( 210 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + O(q^{10}) \) \( 210 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} + 6 q^{15} - 9 q^{17} + 3 q^{19} - 6 q^{21} + 6 q^{23} - 6 q^{25} - 138 q^{27} + 66 q^{29} + 6 q^{31} - 18 q^{33} + 9 q^{35} - 3 q^{37} + 150 q^{39} + 30 q^{41} + 6 q^{43} - 126 q^{45} + 222 q^{47} - 6 q^{49} + 33 q^{51} + 12 q^{55} + 105 q^{57} + 222 q^{59} - 6 q^{61} + 246 q^{63} + 138 q^{65} + 6 q^{67} + 42 q^{69} + 9 q^{71} - 3 q^{73} - 162 q^{75} - 150 q^{77} + 6 q^{79} - 246 q^{81} - 354 q^{83} - 81 q^{85} - 282 q^{87} - 333 q^{89} + 3 q^{91} - 6 q^{93} + 1227 q^{95} + 174 q^{97} + 870 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.3.bc.a 432.bc 27.f $30$ $11.771$ None \(0\) \(6\) \(-15\) \(6\) $\mathrm{SU}(2)[C_{18}]$
432.3.bc.b 432.bc 27.f $36$ $11.771$ None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{18}]$
432.3.bc.c 432.bc 27.f $36$ $11.771$ None \(0\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{18}]$
432.3.bc.d 432.bc 27.f $108$ $11.771$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

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