Properties

Label 432.2.be
Level 432
Weight 2
Character orbit be
Rep. character \(\chi_{432}(47,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 108
Newform subspaces 3
Sturm bound 144
Trace bound 11

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 432.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 468 108 360
Cusp forms 396 108 288
Eisenstein series 72 0 72

Trace form

\( 108q + O(q^{10}) \) \( 108q + 36q^{29} + 18q^{33} + 18q^{41} + 36q^{45} - 18q^{57} - 72q^{65} - 72q^{69} - 72q^{77} - 72q^{81} - 54q^{89} - 72q^{93} + 54q^{97} + O(q^{100}) \)

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.be.a \(36\) \(3.450\) None \(0\) \(0\) \(-6\) \(0\)
432.2.be.b \(36\) \(3.450\) None \(0\) \(0\) \(3\) \(0\)
432.2.be.c \(36\) \(3.450\) None \(0\) \(0\) \(3\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database