Properties

Label 756.2.e
Level 756
Weight 2
Character orbit e
Rep. character \(\chi_{756}(323,\cdot)\)
Character field \(\Q\)
Dimension 48
Newform subspaces 2
Sturm bound 288
Trace bound 4

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Defining parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 156 48 108
Cusp forms 132 48 84
Eisenstein series 24 0 24

Trace form

\( 48q - 4q^{4} + O(q^{10}) \) \( 48q - 4q^{4} + 4q^{10} + 28q^{16} + 8q^{22} - 48q^{25} - 16q^{28} - 28q^{34} + 32q^{37} - 40q^{40} + 36q^{46} - 48q^{49} + 8q^{52} - 20q^{58} - 64q^{61} + 44q^{64} - 12q^{70} - 28q^{82} - 8q^{85} + 40q^{88} + 84q^{94} + O(q^{100}) \)

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.e.a \(24\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)
756.2.e.b \(24\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database