Properties

Label 861.2.l
Level 861
Weight 2
Character orbit l
Rep. character \(\chi_{861}(419,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 216
Newforms 1
Sturm bound 224
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 861 = 3 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 861.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 861 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
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 232 232 0
Cusp forms 216 216 0
Eisenstein series 16 16 0

Trace form

\( 216q + 192q^{4} - 4q^{7} + O(q^{10}) \) \( 216q + 192q^{4} - 4q^{7} + 20q^{15} + 144q^{16} - 24q^{18} - 56q^{22} - 200q^{25} - 40q^{28} + 32q^{30} + 16q^{37} + 4q^{42} - 16q^{51} - 64q^{57} - 32q^{58} + 40q^{60} - 6q^{63} + 48q^{64} - 48q^{67} + 48q^{70} - 92q^{72} + 28q^{78} + 8q^{79} - 120q^{81} + 16q^{85} - 144q^{88} - 16q^{93} + 56q^{99} + O(q^{100}) \)

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.l.a \(216\) \(6.875\) None \(0\) \(0\) \(0\) \(-4\)