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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
87.2.k.a 87.k 87.k $96$ $0.695$ None \(0\) \(-12\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{28}]$