Properties

Label 252.2.ba
Level 252
Weight 2
Character orbit ba
Rep. character \(\chi_{252}(155,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 72
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 36 \)
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 104 72 32
Cusp forms 88 72 16
Eisenstein series 16 0 16

Trace form

\( 72q + 6q^{6} + 4q^{9} + O(q^{10}) \) \( 72q + 6q^{6} + 4q^{9} - 12q^{12} - 34q^{18} - 42q^{20} - 2q^{24} + 36q^{25} + 28q^{30} + 30q^{32} - 44q^{33} - 12q^{34} + 20q^{36} - 12q^{40} - 60q^{41} + 20q^{42} - 24q^{45} - 24q^{46} - 28q^{48} + 36q^{49} - 78q^{50} - 18q^{52} - 10q^{54} - 4q^{57} - 18q^{58} - 76q^{60} - 60q^{64} + 24q^{65} + 54q^{66} + 78q^{68} + 24q^{69} + 74q^{72} - 24q^{73} + 12q^{76} - 20q^{78} - 4q^{81} - 36q^{82} + 14q^{84} + 30q^{86} + 24q^{88} + 8q^{90} - 114q^{92} - 96q^{93} + 42q^{94} + 112q^{96} - 12q^{97} + O(q^{100}) \)

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.ba.a \(72\) \(2.012\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database