Properties

Label 187.2.d
Level 187
Weight 2
Character orbit d
Rep. character \(\chi_{187}(67,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 187 = 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 187.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 20 16 4
Cusp forms 16 16 0
Eisenstein series 4 0 4

Trace form

\( 16q - 2q^{2} + 10q^{4} - 6q^{8} - 20q^{9} + O(q^{10}) \) \( 16q - 2q^{2} + 10q^{4} - 6q^{8} - 20q^{9} - 16q^{13} + 4q^{15} + 6q^{16} + 4q^{17} - 10q^{18} + 20q^{19} + 12q^{21} + 4q^{25} - 12q^{26} + 28q^{30} - 34q^{32} + 4q^{33} - 6q^{34} + 12q^{35} - 18q^{36} + 8q^{43} + 14q^{47} - 42q^{49} - 34q^{50} - 18q^{51} - 44q^{52} + 26q^{53} + 8q^{55} - 30q^{59} + 72q^{60} - 10q^{64} - 8q^{66} + 10q^{67} + 22q^{68} + 4q^{69} - 8q^{70} - 46q^{72} + 36q^{76} - 10q^{77} - 8q^{81} - 8q^{83} + 92q^{84} - 2q^{85} + 56q^{86} + 8q^{87} + 10q^{89} - 20q^{93} + 8q^{94} + 38q^{98} + O(q^{100}) \)

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.d.a \(16\) \(1.493\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-2\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+\beta _{14}q^{3}+(1-\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)