Properties

Label 804.2.j
Level 804
Weight 2
Character orbit j
Rep. character \(\chi_{804}(499,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 136
Newforms 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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 268 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 2 \)
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 280 136 144
Cusp forms 264 136 128
Eisenstein series 16 0 16

Trace form

\( 136q - 4q^{4} + 136q^{9} + O(q^{10}) \) \( 136q - 4q^{4} + 136q^{9} + 12q^{10} + 12q^{13} + 20q^{14} - 4q^{16} - 48q^{20} - 8q^{21} - 44q^{22} + 12q^{24} - 136q^{25} - 20q^{26} - 6q^{28} - 16q^{29} - 24q^{30} + 30q^{32} - 4q^{36} + 24q^{37} - 18q^{38} + 36q^{40} - 36q^{44} + 48q^{46} - 92q^{49} + 18q^{50} - 28q^{56} + 24q^{60} + 12q^{61} - 68q^{62} + 32q^{64} + 68q^{68} + 12q^{73} - 42q^{74} + 28q^{76} - 8q^{77} - 18q^{78} + 30q^{80} + 136q^{81} - 52q^{82} - 8q^{84} - 54q^{86} - 28q^{88} + 12q^{90} + 20q^{92} - 4q^{93} + 36q^{97} - 102q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.2.j.a \(68\) \(6.420\) None \(0\) \(-68\) \(0\) \(4\)
804.2.j.b \(68\) \(6.420\) None \(0\) \(68\) \(0\) \(-4\)

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

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