Properties

Label 252.2.bb
Level 252
Weight 2
Character orbit bb
Rep. character \(\chi_{252}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 88
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.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 252 \)
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 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88q - 2q^{4} - 6q^{5} - 6q^{6} - 2q^{9} + O(q^{10}) \) \( 88q - 2q^{4} - 6q^{5} - 6q^{6} - 2q^{9} + 2q^{10} + 6q^{12} - 4q^{13} - 18q^{14} - 2q^{16} + 2q^{18} - 6q^{20} - 6q^{21} - 6q^{22} - 14q^{24} + 30q^{25} + 6q^{26} - 24q^{29} - 29q^{30} + 10q^{33} - 4q^{34} + 2q^{36} - 4q^{37} - 45q^{38} - 4q^{40} - 12q^{41} - 46q^{42} + 57q^{44} - 18q^{45} - 6q^{46} - 43q^{48} - 2q^{49} + 9q^{50} - 7q^{52} + 23q^{54} - 24q^{56} - 28q^{57} + 5q^{58} - 19q^{60} - 4q^{61} - 8q^{64} + 60q^{66} - 12q^{68} - 6q^{69} - 27q^{70} - 10q^{72} - 4q^{73} + 51q^{74} - 6q^{76} - 30q^{77} + 55q^{78} - 87q^{80} - 34q^{81} - 4q^{82} - 55q^{84} - 14q^{85} + 81q^{86} + 9q^{88} - 60q^{89} + 41q^{90} + 24q^{92} + 30q^{93} - 18q^{94} - 29q^{96} - 4q^{97} + 57q^{98} + O(q^{100}) \)

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.bb.a \(88\) \(2.012\) None \(0\) \(0\) \(-6\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database