Properties

Label 804.2.bf
Level 804
Weight 2
Character orbit bf
Rep. character \(\chi_{804}(7,\cdot)\)
Character field \(\Q(\zeta_{66})\)
Dimension 1360
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.bf (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 268 \)
Character field: \(\Q(\zeta_{66})\)
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 2800 1360 1440
Cusp forms 2640 1360 1280
Eisenstein series 160 0 160

Trace form

\( 1360q + 4q^{4} - 66q^{8} - 136q^{9} + O(q^{10}) \) \( 1360q + 4q^{4} - 66q^{8} - 136q^{9} + 54q^{10} - 12q^{13} - 20q^{14} + 4q^{16} + 48q^{20} + 8q^{21} + 66q^{22} - 12q^{24} + 136q^{25} + 20q^{26} - 16q^{28} + 16q^{29} + 24q^{30} + 80q^{32} - 18q^{36} - 24q^{37} + 18q^{38} + 74q^{40} + 36q^{44} - 26q^{46} + 92q^{49} + 48q^{50} + 28q^{56} - 132q^{57} - 24q^{60} - 12q^{61} + 68q^{62} - 98q^{64} + 416q^{68} - 144q^{73} + 42q^{74} - 28q^{76} + 8q^{77} + 18q^{78} - 30q^{80} - 136q^{81} - 168q^{82} + 8q^{84} - 166q^{86} + 28q^{88} + 54q^{90} - 20q^{92} + 4q^{93} - 36q^{97} + 102q^{98} + O(q^{100}) \)

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.bf.a \(680\) \(6.420\) None \(0\) \(-68\) \(0\) \(4\)
804.2.bf.b \(680\) \(6.420\) None \(0\) \(68\) \(0\) \(-4\)

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

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