Properties

Label 756.2.cd
Level 756
Weight 2
Character orbit cd
Rep. character \(\chi_{756}(31,\cdot)\)
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.cd (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

\( 840q - 3q^{2} - 3q^{4} - 18q^{5} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 840q - 3q^{2} - 3q^{4} - 18q^{5} - 6q^{8} - 6q^{9} - 9q^{10} - 9q^{12} + 24q^{14} - 3q^{16} - 18q^{17} - 3q^{18} - 12q^{21} - 12q^{22} - 36q^{24} - 6q^{25} - 18q^{26} - 12q^{28} - 36q^{29} + 15q^{30} - 63q^{32} - 18q^{33} - 18q^{34} + 18q^{36} - 12q^{37} - 9q^{38} - 9q^{40} + 9q^{42} - 6q^{44} + 18q^{45} - 6q^{46} - 12q^{49} + 3q^{50} - 9q^{52} - 12q^{53} - 135q^{54} + 15q^{56} - 42q^{57} - 3q^{58} + 57q^{60} - 18q^{61} + 99q^{62} - 6q^{64} - 54q^{65} - 9q^{66} - 54q^{68} - 72q^{69} + 9q^{70} + 87q^{72} - 69q^{74} + 36q^{76} - 36q^{77} + 6q^{78} - 18q^{80} + 42q^{81} - 18q^{82} - 87q^{84} + 6q^{85} - 117q^{86} + 21q^{88} - 18q^{89} - 81q^{90} + 48q^{92} - 6q^{93} - 9q^{94} - 9q^{96} + 54q^{98} + O(q^{100}) \)

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.cd.a \(840\) \(6.037\) None \(-3\) \(0\) \(-18\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database