Properties

Label 806.2.bn
Level 806
Weight 2
Character orbit bn
Rep. character \(\chi_{806}(151,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 320
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.bn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{20})\)
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 928 320 608
Cusp forms 864 320 544
Eisenstein series 64 0 64

Trace form

\( 320q + 16q^{7} + 96q^{9} + O(q^{10}) \) \( 320q + 16q^{7} + 96q^{9} - 20q^{11} - 20q^{13} + 12q^{14} + 80q^{16} + 16q^{18} - 32q^{19} - 60q^{21} - 60q^{27} - 24q^{28} + 4q^{31} + 52q^{33} - 40q^{34} - 40q^{35} + 44q^{39} + 28q^{41} + 40q^{46} - 32q^{47} - 40q^{53} + 4q^{59} + 104q^{63} + 40q^{65} + 32q^{66} - 32q^{67} - 24q^{70} + 8q^{71} - 16q^{72} - 48q^{76} - 76q^{78} + 80q^{79} - 272q^{81} - 40q^{83} + 40q^{84} + 80q^{85} + 32q^{87} - 80q^{89} - 200q^{91} - 100q^{93} - 8q^{94} + 52q^{97} + 48q^{98} + O(q^{100}) \)

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.bn.a \(320\) \(6.436\) None \(0\) \(0\) \(0\) \(16\)

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

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