Properties

Label 806.2.ba
Level 806
Weight 2
Character orbit ba
Rep. character \(\chi_{806}(119,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 152
Newforms 1
Sturm bound 224
Trace bound 0

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Defining parameters

Level: \( N \) = \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 806.ba (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{12})\)
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 464 152 312
Cusp forms 432 152 280
Eisenstein series 32 0 32

Trace form

\( 152q - 12q^{7} - 160q^{9} + O(q^{10}) \) \( 152q - 12q^{7} - 160q^{9} + 12q^{11} - 4q^{12} + 4q^{14} + 76q^{16} - 12q^{17} + 16q^{18} - 28q^{19} + 20q^{21} - 12q^{26} + 12q^{28} - 12q^{29} + 20q^{31} + 28q^{33} - 24q^{34} - 4q^{35} - 28q^{37} - 72q^{38} + 20q^{39} + 36q^{41} - 36q^{42} - 16q^{43} - 12q^{44} - 84q^{45} - 24q^{46} - 8q^{47} + 36q^{49} + 24q^{51} - 8q^{52} - 12q^{53} + 8q^{57} - 12q^{58} - 24q^{59} - 12q^{61} - 36q^{62} + 4q^{63} + 120q^{65} + 32q^{66} - 52q^{67} + 48q^{69} + 48q^{70} - 76q^{71} - 16q^{72} - 52q^{73} + 48q^{74} + 92q^{75} + 4q^{76} + 96q^{77} + 12q^{78} + 12q^{79} + 120q^{81} + 28q^{84} - 24q^{85} - 36q^{86} + 64q^{87} - 12q^{89} - 44q^{91} + 120q^{93} - 8q^{94} - 124q^{97} + 40q^{98} + O(q^{100}) \)

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.ba.a \(152\) \(6.436\) None \(0\) \(0\) \(0\) \(-12\)

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

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