Properties

Label 187.2.h
Level 187
Weight 2
Character orbit h
Rep. character \(\chi_{187}(100,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 56
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.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
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 80 56 24
Cusp forms 64 56 8
Eisenstein series 16 0 16

Trace form

\( 56q - 16q^{6} + O(q^{10}) \) \( 56q - 16q^{6} - 16q^{10} - 16q^{14} + 24q^{15} - 32q^{16} + 8q^{17} - 24q^{19} + 16q^{20} - 24q^{24} - 8q^{25} - 48q^{27} - 40q^{32} + 16q^{33} + 64q^{34} + 32q^{35} + 64q^{36} + 8q^{37} - 32q^{39} + 96q^{40} - 24q^{41} - 8q^{42} - 32q^{43} + 16q^{44} - 32q^{45} - 16q^{46} - 24q^{48} - 112q^{50} - 48q^{51} + 8q^{53} - 72q^{54} + 64q^{56} + 40q^{57} + 16q^{58} + 16q^{59} - 8q^{60} - 64q^{61} + 56q^{62} + 16q^{63} + 56q^{65} + 24q^{67} - 88q^{68} - 64q^{69} - 96q^{70} - 16q^{71} + 8q^{73} - 48q^{74} + 40q^{75} + 88q^{76} + 136q^{78} - 32q^{80} + 104q^{82} - 56q^{83} + 80q^{84} - 8q^{85} - 32q^{86} + 56q^{87} - 32q^{91} + 40q^{92} + 8q^{93} + 16q^{94} + 48q^{95} + 64q^{96} - 16q^{97} + O(q^{100}) \)

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.h.a \(56\) \(1.493\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(187, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(187, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)