Properties

Label 756.2.cf
Level 756
Weight 2
Character orbit cf
Rep. character \(\chi_{756}(155,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 648
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.cf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 108 \)
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 888 648 240
Cusp forms 840 648 192
Eisenstein series 48 0 48

Trace form

\( 648q + O(q^{10}) \) \( 648q + 18q^{12} + 42q^{18} + 42q^{20} - 48q^{30} - 30q^{32} + 60q^{33} + 60q^{41} - 30q^{42} - 144q^{44} - 18q^{48} - 156q^{50} + 54q^{52} - 12q^{57} + 54q^{58} - 186q^{60} - 24q^{65} - 186q^{66} - 78q^{68} - 42q^{72} - 24q^{81} - 30q^{86} - 36q^{89} + 198q^{90} + 114q^{92} - 144q^{93} - 54q^{94} + 156q^{96} + 36q^{97} + O(q^{100}) \)

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.cf.a \(648\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database