Properties

Label 432.2.l
Level 432
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
432.2.l.a \(32\) \(3.450\) None \(0\) \(0\) \(0\) \(0\)
432.2.l.b \(32\) \(3.450\) None \(0\) \(0\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database