Properties

Label 252.2.be
Level 252
Weight 2
Character orbit be
Rep. character \(\chi_{252}(107,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 32
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 252.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 112 32 80
Cusp forms 80 32 48
Eisenstein series 32 0 32

Trace form

\( 32q + O(q^{10}) \) \( 32q + 16q^{13} + 4q^{16} - 32q^{22} + 24q^{25} - 44q^{28} - 16q^{34} + 8q^{37} - 52q^{40} - 24q^{46} - 16q^{49} - 52q^{52} - 12q^{58} - 16q^{61} + 120q^{64} + 60q^{70} - 8q^{73} + 72q^{76} + 68q^{82} - 32q^{85} + 44q^{88} + 60q^{94} - 176q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.be.a \(32\) \(2.012\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database