Properties

Label 87.1.d
Level $87$
Weight $1$
Character orbit 87.d
Rep. character $\chi_{87}(86,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $10$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 87.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 87 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(87, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q - 2 q^{6} - 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{6} - 2 q^{7} + 2 q^{9} - 2 q^{13} - 2 q^{16} + 2 q^{22} + 2 q^{24} + 2 q^{25} - 2 q^{33} + 2 q^{34} + 2 q^{42} - 2 q^{51} - 2 q^{54} - 2 q^{58} - 2 q^{63} + 2 q^{64} - 2 q^{67} + 2 q^{78} + 2 q^{81} - 4 q^{82} + 2 q^{87} - 2 q^{88} + 2 q^{91} + 2 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(87, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
87.1.d.a 87.d 87.d $1$ $0.043$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-87}) \) None 87.1.d.a \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
87.1.d.b 87.d 87.d $1$ $0.043$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-87}) \) None 87.1.d.a \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)