Properties

Label 804.2.u
Level 804
Weight 2
Character orbit u
Rep. character \(\chi_{804}(43,\cdot)\)
Character field \(\Q(\zeta_{22})\)
Dimension 680
Newforms 2
Sturm bound 272
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.u (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 268 \)
Character field: \(\Q(\zeta_{22})\)
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 1400 680 720
Cusp forms 1320 680 640
Eisenstein series 80 0 80

Trace form

\( 680q - 4q^{4} + 66q^{8} - 68q^{9} + O(q^{10}) \) \( 680q - 4q^{4} + 66q^{8} - 68q^{9} - 54q^{10} + 8q^{14} - 4q^{16} - 8q^{21} - 6q^{22} + 12q^{24} + 68q^{25} - 20q^{26} + 22q^{28} + 32q^{29} - 110q^{32} + 18q^{36} - 24q^{37} - 74q^{40} - 22q^{46} - 92q^{49} - 66q^{50} - 28q^{56} + 132q^{57} + 24q^{60} + 4q^{62} + 14q^{64} - 416q^{68} + 108q^{73} + 64q^{76} + 16q^{77} - 68q^{81} + 168q^{82} + 16q^{84} + 208q^{86} + 56q^{88} - 54q^{90} + 92q^{92} + 8q^{93} + O(q^{100}) \)

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.u.a \(340\) \(6.420\) None \(0\) \(-34\) \(0\) \(-4\)
804.2.u.b \(340\) \(6.420\) None \(0\) \(34\) \(0\) \(4\)

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

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