Properties

Label 95.1.d
Level 95
Weight 1
Character orbit d
Rep. character \(\chi_{95}(94,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 10
Trace bound 1

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 95.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 95 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(95, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 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 3 0 0 0

Trace form

\(3q \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut +\mathstrut 3q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 3q^{64} \) \(\mathstrut -\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 3q^{76} \) \(\mathstrut +\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(95, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
95.1.d.a \(1\) \(0.047\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
95.1.d.b \(2\) \(0.047\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)