Properties

Label 806.2.bf
Level 806
Weight 2
Character orbit bf
Rep. character \(\chi_{806}(57,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 144
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.bf (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 464 144 320
Cusp forms 432 144 288
Eisenstein series 32 0 32

Trace form

\( 144q - 4q^{7} + 64q^{9} + O(q^{10}) \) \( 144q - 4q^{7} + 64q^{9} + 12q^{11} + 4q^{14} - 144q^{16} + 16q^{18} + 48q^{21} - 12q^{22} + 12q^{26} - 4q^{28} - 16q^{31} - 8q^{33} - 24q^{34} + 8q^{35} - 60q^{37} + 48q^{39} + 36q^{42} + 12q^{44} + 36q^{45} - 8q^{47} - 12q^{53} + 36q^{57} + 24q^{59} - 112q^{63} - 144q^{65} + 32q^{66} + 48q^{70} + 20q^{71} - 16q^{72} + 48q^{73} - 48q^{74} - 120q^{78} - 96q^{79} - 56q^{81} - 96q^{83} + 48q^{84} + 84q^{86} - 128q^{87} + 56q^{93} + 16q^{94} - 48q^{97} - 8q^{98} + 60q^{99} + O(q^{100}) \)

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.bf.a \(144\) \(6.436\) None \(0\) \(0\) \(0\) \(-4\)

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

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