Properties

Label 95.1.d
Level 95
Weight 1
Character orbit 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

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

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

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 \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
$3$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
$5$ (\( 1 - T \))(\( ( 1 + T )^{2} \))
$7$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$11$ (\( ( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$13$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
$17$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$19$ (\( 1 - T \))(\( ( 1 + T )^{2} \))
$23$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$29$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$31$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$37$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
$41$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$43$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$47$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$53$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
$59$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$61$ (\( ( 1 + T )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$67$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
$71$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$73$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$79$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$83$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$89$ (\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$97$ (\( 1 + T^{2} \))(\( 1 + T^{4} \))
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