Properties

Label 87.1.d
Level 87
Weight 1
Character orbit d
Rep. character \(\chi_{87}(86,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(87, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
87.1.d.a \(1\) \(0.043\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-87}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
87.1.d.b \(1\) \(0.043\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-87}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)