Properties

Label 861.2.bo
Level 861
Weight 2
Character orbit bo
Rep. character \(\chi_{861}(43,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 352
Newforms 2
Sturm bound 224
Trace bound 1

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Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 861.bo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).

Total New Old
Modular forms 928 352 576
Cusp forms 864 352 512
Eisenstein series 64 0 64

Trace form

\( 352q + 96q^{4} + O(q^{10}) \) \( 352q + 96q^{4} + 48q^{10} - 8q^{11} + 16q^{12} + 8q^{13} + 32q^{15} - 112q^{16} + 16q^{17} - 8q^{19} - 8q^{22} + 24q^{23} + 56q^{25} - 16q^{26} + 24q^{30} - 32q^{31} - 24q^{34} + 8q^{35} - 8q^{37} + 96q^{38} + 64q^{40} - 8q^{41} + 32q^{42} - 8q^{44} + 16q^{45} - 80q^{46} + 88q^{47} - 32q^{48} - 24q^{51} - 104q^{52} - 40q^{53} + 136q^{55} + 8q^{57} + 8q^{58} + 32q^{60} + 144q^{64} + 192q^{65} - 80q^{66} + 24q^{67} - 64q^{68} + 40q^{69} - 8q^{70} - 136q^{71} + 80q^{74} + 48q^{75} - 72q^{76} - 136q^{78} - 32q^{79} - 400q^{80} - 352q^{81} + 184q^{82} + 32q^{85} - 192q^{86} - 80q^{87} + 24q^{88} - 40q^{89} - 240q^{92} - 72q^{93} - 64q^{94} - 80q^{95} - 40q^{96} + 112q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
861.2.bo.a \(160\) \(6.875\) None \(0\) \(0\) \(0\) \(0\)
861.2.bo.b \(192\) \(6.875\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(861, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)