Properties

Label 861.2.e
Level 861
Weight 2
Character orbit e
Rep. character \(\chi_{861}(860,\cdot)\)
Character field \(\Q\)
Dimension 108
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 861 \)
Character field: \(\Q\)
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 116 116 0
Cusp forms 108 108 0
Eisenstein series 8 8 0

Trace form

\( 108q - 112q^{4} + 4q^{9} + O(q^{10}) \) \( 108q - 112q^{4} + 4q^{9} + 104q^{16} + 4q^{18} - 16q^{21} + 76q^{25} - 56q^{36} - 16q^{37} - 36q^{39} + 24q^{42} - 16q^{43} - 96q^{46} + 20q^{49} - 12q^{51} - 36q^{57} - 80q^{64} - 14q^{72} - 46q^{78} - 52q^{81} + 30q^{84} - 48q^{91} + O(q^{100}) \)

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.e.a \(28\) \(6.875\) \(\Q(\sqrt{-287}) \) \(0\) \(0\) \(0\) \(0\)
861.2.e.b \(80\) \(6.875\) None \(0\) \(0\) \(0\) \(0\)