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Properties

Label 432.2.l
Level $432$
Weight $2$
Character orbit 432.l
Rep. character $\chi_{432}(107,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $2$
Sturm bound $144$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

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

\( 64 q + O(q^{10}) \) \( 64 q + 4 q^{10} - 28 q^{16} - 8 q^{19} + 20 q^{22} + 12 q^{28} - 12 q^{34} - 36 q^{40} + 16 q^{43} + 16 q^{46} + 64 q^{49} - 12 q^{52} + 32 q^{55} - 48 q^{58} + 16 q^{61} + 24 q^{64} - 64 q^{67} - 72 q^{70} - 144 q^{76} - 40 q^{82} + 16 q^{85} + 12 q^{88} - 24 q^{91} - 36 q^{94} + O(q^{100}) \)

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.l.a 432.l 48.k $32$ $3.450$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
432.2.l.b 432.l 48.k $32$ $3.450$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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