Properties

Label 87.2.k
Level $87$
Weight $2$
Character orbit 87.k
Rep. character $\chi_{87}(2,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $96$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 87.k (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 87 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(87, [\chi])\).

Total New Old
Modular forms 144 144 0
Cusp forms 96 96 0
Eisenstein series 48 48 0

Trace form

\( 96q - 12q^{3} - 28q^{4} - 14q^{6} - 20q^{7} - 14q^{9} + O(q^{10}) \) \( 96q - 12q^{3} - 28q^{4} - 14q^{6} - 20q^{7} - 14q^{9} - 4q^{10} - 8q^{12} - 28q^{13} - 16q^{15} - 48q^{16} - 28q^{18} - 20q^{19} + 26q^{21} - 28q^{22} + 58q^{24} - 20q^{25} + 36q^{27} + 96q^{30} - 32q^{31} + 28q^{33} - 28q^{34} + 22q^{36} - 4q^{37} - 40q^{39} - 48q^{40} - 14q^{42} - 32q^{43} + 42q^{45} + 120q^{46} - 20q^{48} + 4q^{49} - 14q^{51} + 72q^{52} - 30q^{54} + 148q^{55} + 112q^{58} + 20q^{60} + 12q^{61} - 14q^{63} + 224q^{64} - 32q^{66} + 28q^{67} + 10q^{69} + 52q^{70} - 44q^{72} + 16q^{73} - 144q^{75} - 100q^{76} - 102q^{78} - 60q^{79} - 146q^{81} - 108q^{82} - 64q^{84} - 104q^{85} - 70q^{87} - 312q^{88} - 96q^{90} - 112q^{91} - 70q^{93} + 56q^{94} - 168q^{96} + 32q^{97} + 82q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(87, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
87.2.k.a \(96\) \(0.695\) None \(0\) \(-12\) \(0\) \(-20\)