Properties

Label 861.2.cg
Level 861
Weight 2
Character orbit cg
Rep. character \(\chi_{861}(5,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 1728
Newform subspaces 1
Sturm bound 224
Trace bound 0

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Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 861.cg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 861 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

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

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

Trace form

\( 1728q - 24q^{3} + 196q^{4} - 32q^{7} + O(q^{10}) \) \( 1728q - 24q^{3} + 196q^{4} - 32q^{7} - 36q^{10} - 36q^{12} - 8q^{15} + 196q^{16} + 18q^{18} - 48q^{19} - 20q^{21} - 88q^{22} + 6q^{24} - 196q^{25} - 68q^{28} + 2q^{30} - 36q^{31} - 180q^{33} - 120q^{36} + 12q^{37} - 10q^{39} - 24q^{40} - 104q^{42} - 80q^{43} - 66q^{45} + 80q^{46} - 40q^{49} - 48q^{51} - 60q^{52} - 120q^{54} - 80q^{57} + 8q^{58} + 138q^{60} - 60q^{61} - 30q^{63} - 384q^{64} - 150q^{66} - 8q^{67} - 24q^{70} - 50q^{72} + 108q^{75} + 96q^{78} - 24q^{79} + 40q^{81} - 312q^{82} - 40q^{84} + 8q^{85} - 30q^{87} + 112q^{88} + 84q^{93} - 168q^{94} - 24q^{96} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
861.2.cg.a \(1728\) \(6.875\) None \(0\) \(-24\) \(0\) \(-32\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database