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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

\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist 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 87.2.k.a \(0\) \(-12\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{28}]$