Properties

Label 756.2.bs
Level 756
Weight 2
Character orbit bs
Rep. character \(\chi_{756}(11,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 840
Newform subspaces 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.bs (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 756 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 888 888 0
Cusp forms 840 840 0
Eisenstein series 48 48 0

Trace form

\( 840q - 3q^{2} - 3q^{4} - 6q^{5} - 12q^{6} - 18q^{8} - 6q^{9} + O(q^{10}) \) \( 840q - 3q^{2} - 3q^{4} - 6q^{5} - 12q^{6} - 18q^{8} - 6q^{9} - 6q^{10} - 3q^{12} - 24q^{13} - 21q^{14} - 3q^{16} - 3q^{18} - 12q^{20} - 12q^{21} - 12q^{22} - 15q^{24} - 6q^{25} - 12q^{28} - 12q^{29} + 33q^{30} + 27q^{32} - 6q^{33} - 6q^{34} - 42q^{36} + 6q^{37} - 9q^{38} + 12q^{40} - 24q^{41} - 21q^{42} - 9q^{44} - 30q^{45} + 3q^{46} - 78q^{48} - 12q^{49} - 27q^{50} - 3q^{52} + 39q^{54} - 27q^{56} - 6q^{57} - 3q^{58} + 27q^{60} - 6q^{61} - 117q^{62} - 6q^{64} + 18q^{65} - 3q^{66} + 60q^{68} - 48q^{69} + 24q^{70} - 63q^{72} + 6q^{73} - 75q^{74} + 12q^{77} + 6q^{78} + 18q^{81} - 6q^{82} + 132q^{84} + 6q^{85} - 81q^{86} + 45q^{88} - 39q^{90} + 48q^{92} - 6q^{93} - 3q^{94} - 111q^{96} - 24q^{97} - 9q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
756.2.bs.a \(840\) \(6.037\) None \(-3\) \(0\) \(-6\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database