Properties

Label 756.2.bf
Level 756
Weight 2
Character orbit bf
Rep. character \(\chi_{756}(271,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 128
Newform subspaces 4
Sturm bound 288
Trace bound 11

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Defining parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 312 128 184
Cusp forms 264 128 136
Eisenstein series 48 0 48

Trace form

\( 128q + O(q^{10}) \) \( 128q - 16q^{16} + 44q^{22} + 68q^{25} - 22q^{28} + 4q^{37} + 30q^{40} - 6q^{46} + 8q^{49} + 18q^{52} - 20q^{58} + 12q^{64} - 90q^{70} + 36q^{73} - 6q^{82} + 16q^{85} - 8q^{88} - 54q^{94} + O(q^{100}) \)

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.bf.a \(32\) \(6.037\) None \(0\) \(0\) \(0\) \(-2\)
756.2.bf.b \(32\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)
756.2.bf.c \(32\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)
756.2.bf.d \(32\) \(6.037\) None \(0\) \(0\) \(0\) \(2\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database