Properties

Label 756.2.bb
Level 756
Weight 2
Character orbit bb
Rep. character \(\chi_{756}(611,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 88
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.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 252 \)
Character field: \(\Q(\zeta_{6})\)
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 312 104 208
Cusp forms 264 88 176
Eisenstein series 48 16 32

Trace form

\( 88q - 2q^{4} + 6q^{5} + O(q^{10}) \) \( 88q - 2q^{4} + 6q^{5} + 2q^{10} - 4q^{13} + 18q^{14} - 2q^{16} + 6q^{20} - 6q^{22} + 30q^{25} - 6q^{26} + 24q^{29} - 4q^{34} - 4q^{37} + 45q^{38} - 4q^{40} + 12q^{41} - 57q^{44} - 6q^{46} - 2q^{49} - 9q^{50} - 7q^{52} + 24q^{56} + 5q^{58} - 4q^{61} - 8q^{64} + 12q^{68} - 27q^{70} - 4q^{73} - 51q^{74} - 6q^{76} + 30q^{77} + 87q^{80} - 4q^{82} - 14q^{85} - 81q^{86} + 9q^{88} + 60q^{89} - 24q^{92} - 18q^{94} - 4q^{97} - 57q^{98} + O(q^{100}) \)

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.bb.a \(88\) \(6.037\) None \(0\) \(0\) \(6\) \(0\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database