Properties

Label 432.2.i
Level $432$
Weight $2$
Character orbit 432.i
Rep. character $\chi_{432}(145,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $4$
Sturm bound $144$
Trace bound $5$

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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

\( 10 q + q^{5} + q^{7} + O(q^{10}) \) \( 10 q + q^{5} + q^{7} - 7 q^{11} - q^{13} + 8 q^{17} + 4 q^{19} + 5 q^{23} - 2 q^{25} - 3 q^{29} + 7 q^{31} + 30 q^{35} - 4 q^{37} + 3 q^{41} + 7 q^{43} + 15 q^{47} + 4 q^{53} - 6 q^{55} - 25 q^{59} - q^{61} - 17 q^{65} + q^{67} - 56 q^{71} - 16 q^{73} - 21 q^{77} + q^{79} - 29 q^{83} - 6 q^{85} - 12 q^{89} - 22 q^{91} + 28 q^{95} + 5 q^{97} + O(q^{100}) \)

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.i.a 432.i 9.c $2$ $3.450$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
432.2.i.b 432.i 9.c $2$ $3.450$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots\)
432.2.i.c 432.i 9.c $2$ $3.450$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
432.2.i.d 432.i 9.c $4$ $3.450$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)

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

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