Properties

Label 804.2.e
Level 804
Weight 2
Character orbit e
Rep. character \(\chi_{804}(535,\cdot)\)
Character field \(\Q\)
Dimension 68
Newform subspaces 2
Sturm bound 272
Trace bound 3

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Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 268 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(272\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).

Total New Old
Modular forms 140 68 72
Cusp forms 132 68 64
Eisenstein series 8 0 8

Trace form

\( 68q + 4q^{4} + 68q^{9} + O(q^{10}) \) \( 68q + 4q^{4} + 68q^{9} - 12q^{10} - 8q^{14} + 4q^{16} + 8q^{21} - 16q^{22} - 12q^{24} - 68q^{25} + 20q^{26} - 32q^{29} + 4q^{36} + 24q^{37} - 36q^{40} + 92q^{49} + 28q^{56} - 24q^{60} - 4q^{62} + 52q^{64} - 68q^{68} + 24q^{73} - 64q^{76} - 16q^{77} + 68q^{81} + 52q^{82} - 16q^{84} + 12q^{86} - 56q^{88} - 12q^{90} - 92q^{92} - 8q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.2.e.a \(34\) \(6.420\) None \(0\) \(-34\) \(0\) \(-4\)
804.2.e.b \(34\) \(6.420\) None \(0\) \(34\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(804, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database