Properties

Label 95.1.d
Level $95$
Weight $1$
Character orbit 95.d
Rep. character $\chi_{95}(94,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.1.d.a 95.d 95.d $1$ $0.047$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) 95.1.d.a \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
95.1.d.b 95.d 95.d $2$ $0.047$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-95}) \) None 95.1.d.b \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)