Properties

Label 756.2.ba
Level 756
Weight 2
Character orbit ba
Rep. character \(\chi_{756}(71,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 72
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 36 \)
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 72 240
Cusp forms 264 72 192
Eisenstein series 48 0 48

Trace form

\( 72q + O(q^{10}) \) \( 72q + 42q^{20} + 36q^{25} - 30q^{32} - 12q^{34} - 12q^{40} + 60q^{41} - 24q^{46} + 36q^{49} + 78q^{50} - 18q^{52} - 18q^{58} - 60q^{64} - 24q^{65} - 78q^{68} - 24q^{73} + 12q^{76} - 36q^{82} - 30q^{86} + 24q^{88} + 114q^{92} + 42q^{94} - 12q^{97} + O(q^{100}) \)

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.ba.a \(72\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database