Properties

Label 432.2.k
Level $432$
Weight $2$
Character orbit 432.k
Rep. character $\chi_{432}(109,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $4$
Sturm bound $144$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

Total New Old
Modular forms 156 64 92
Cusp forms 132 64 68
Eisenstein series 24 0 24

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 4 q^{10} + 36 q^{16} + 8 q^{19} + 4 q^{22} + 12 q^{28} + 20 q^{34} + 4 q^{40} + 16 q^{43} - 48 q^{46} - 64 q^{49} - 20 q^{52} - 48 q^{58} - 16 q^{61} - 24 q^{64} + 64 q^{67} - 120 q^{70} - 48 q^{76} - 16 q^{79} + 16 q^{85} - 116 q^{88} - 24 q^{91} - 12 q^{94} + O(q^{100}) \)

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.k.a 432.k 16.e $4$ $3.450$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.b 432.k 16.e $4$ $3.450$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.c 432.k 16.e $24$ $3.450$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
432.2.k.d 432.k 16.e $32$ $3.450$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)