Properties

Label 187.2.e
Level 187
Weight 2
Character orbit e
Rep. character \(\chi_{187}(89,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 32
Newforms 2
Sturm bound 36
Trace bound 1

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Defining parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(187, [\chi])\).

Total New Old
Modular forms 40 32 8
Cusp forms 32 32 0
Eisenstein series 8 0 8

Trace form

\( 32q - 36q^{4} - 8q^{5} + 8q^{6} + O(q^{10}) \) \( 32q - 36q^{4} - 8q^{5} + 8q^{6} + 4q^{10} - 20q^{12} - 12q^{14} + 28q^{16} - 12q^{17} - 20q^{18} + 12q^{20} + 24q^{21} - 4q^{23} + 12q^{24} + 12q^{27} - 52q^{28} + 12q^{29} + 24q^{30} - 24q^{31} + 8q^{33} + 16q^{34} - 32q^{35} - 20q^{37} - 40q^{38} - 8q^{39} - 20q^{40} + 16q^{41} + 8q^{44} + 48q^{45} + 36q^{46} - 4q^{47} + 60q^{48} + 36q^{50} + 56q^{51} - 16q^{55} + 64q^{56} - 32q^{57} - 64q^{58} - 8q^{61} + 52q^{62} + 20q^{63} + 20q^{64} - 48q^{65} - 12q^{67} - 32q^{68} - 64q^{69} + 28q^{71} + 20q^{72} + 20q^{73} + 68q^{74} + 4q^{78} + 16q^{79} - 48q^{80} - 80q^{81} - 12q^{82} - 168q^{84} + 24q^{85} + 8q^{86} + 12q^{89} - 104q^{90} + 8q^{91} + 68q^{92} - 36q^{95} - 140q^{96} - 16q^{97} + 116q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(187, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
187.2.e.a \(4\) \(1.493\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(8\) \(0\) \(q+2\zeta_{8}^{2}q^{2}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{3}+\cdots\)
187.2.e.b \(28\) \(1.493\) None \(0\) \(4\) \(-16\) \(0\)