Properties

Label 756.2.cc
Level 756
Weight 2
Character orbit cc
Rep. character \(\chi_{756}(139,\cdot)\)
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.cc (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

\( 840q - 12q^{2} - 12q^{4} - 6q^{8} - 24q^{9} + O(q^{10}) \) \( 840q - 12q^{2} - 12q^{4} - 6q^{8} - 24q^{9} - 21q^{14} - 12q^{16} - 12q^{18} - 12q^{21} - 12q^{22} - 24q^{25} - 12q^{28} + 6q^{30} + 18q^{32} - 72q^{36} - 12q^{37} - 36q^{42} - 6q^{44} - 6q^{46} - 12q^{49} - 42q^{50} - 48q^{53} - 111q^{56} + 12q^{57} - 12q^{58} - 42q^{60} - 6q^{64} + 9q^{70} + 78q^{72} - 42q^{74} - 36q^{77} - 48q^{78} - 48q^{81} - 114q^{84} - 84q^{85} + 126q^{86} - 60q^{88} - 132q^{92} - 24q^{93} + 54q^{98} + O(q^{100}) \)

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.cc.a \(840\) \(6.037\) None \(-12\) \(0\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database