Properties

Label 806.2.cb
Level 806
Weight 2
Character orbit cb
Rep. character \(\chi_{806}(137,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 608
Newforms 1
Sturm bound 224
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 806.cb (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{60})\)
Newforms: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).

Total New Old
Modular forms 1856 608 1248
Cusp forms 1728 608 1120
Eisenstein series 128 0 128

Trace form

\( 608q - 12q^{7} - 80q^{9} + O(q^{10}) \) \( 608q - 12q^{7} - 80q^{9} + 8q^{11} - 4q^{12} + 20q^{13} - 24q^{14} - 76q^{16} + 24q^{17} + 32q^{18} + 4q^{19} - 112q^{21} - 12q^{22} + 60q^{27} + 32q^{28} - 12q^{29} - 16q^{31} + 92q^{33} - 56q^{34} + 4q^{35} - 4q^{37} + 108q^{38} - 120q^{39} + 8q^{41} - 48q^{43} - 48q^{45} - 64q^{46} + 8q^{47} + 24q^{51} + 4q^{52} + 52q^{53} - 148q^{57} - 12q^{58} - 4q^{59} - 12q^{61} + 36q^{62} - 204q^{63} + 128q^{65} - 32q^{66} + 52q^{67} - 180q^{69} - 48q^{70} - 8q^{71} - 32q^{72} - 4q^{73} + 116q^{75} + 52q^{76} - 144q^{77} - 92q^{78} + 28q^{79} + 220q^{81} - 56q^{83} - 48q^{84} - 104q^{85} - 12q^{86} - 32q^{87} + 128q^{89} - 104q^{91} - 172q^{93} + 8q^{94} + 84q^{97} - 72q^{98} - 240q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
806.2.cb.a \(608\) \(6.436\) None \(0\) \(0\) \(0\) \(-12\)

Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)