Properties

Label 95.1.d.a
Level 95
Weight 1
Character orbit 95.d
Self dual yes
Analytic conductor 0.047
Analytic rank 0
Dimension 1
Projective image \(D_{2}\)
CM/RM discs -19, -95, 5
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 95.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0474111762001\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{2}\)
Projective field Galois closure of \(\Q(\sqrt{5}, \sqrt{-19})\)
Artin image $D_4$
Artin field Galois closure of 4.2.475.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{4} + q^{5} - q^{9} + O(q^{10}) \) \( q - q^{4} + q^{5} - q^{9} - 2q^{11} + q^{16} + q^{19} - q^{20} + q^{25} + q^{36} + 2q^{44} - q^{45} + q^{49} - 2q^{55} - 2q^{61} - q^{64} - q^{76} + q^{80} + q^{81} + q^{95} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(-1\) \(-1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
94.1
0
0 0 −1.00000 1.00000 0 0 0 −1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 RM by \(\Q(\sqrt{5}) \)
19.b odd 2 1 CM by \(\Q(\sqrt{-19}) \)
95.d odd 2 1 CM by \(\Q(\sqrt{-95}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.1.d.a 1
3.b odd 2 1 855.1.g.a 1
4.b odd 2 1 1520.1.m.a 1
5.b even 2 1 RM 95.1.d.a 1
5.c odd 4 2 475.1.c.a 1
15.d odd 2 1 855.1.g.a 1
19.b odd 2 1 CM 95.1.d.a 1
19.c even 3 2 1805.1.h.a 2
19.d odd 6 2 1805.1.h.a 2
19.e even 9 6 1805.1.o.a 6
19.f odd 18 6 1805.1.o.a 6
20.d odd 2 1 1520.1.m.a 1
57.d even 2 1 855.1.g.a 1
76.d even 2 1 1520.1.m.a 1
95.d odd 2 1 CM 95.1.d.a 1
95.g even 4 2 475.1.c.a 1
95.h odd 6 2 1805.1.h.a 2
95.i even 6 2 1805.1.h.a 2
95.o odd 18 6 1805.1.o.a 6
95.p even 18 6 1805.1.o.a 6
285.b even 2 1 855.1.g.a 1
380.d even 2 1 1520.1.m.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.1.d.a 1 1.a even 1 1 trivial
95.1.d.a 1 5.b even 2 1 RM
95.1.d.a 1 19.b odd 2 1 CM
95.1.d.a 1 95.d odd 2 1 CM
475.1.c.a 1 5.c odd 4 2
475.1.c.a 1 95.g even 4 2
855.1.g.a 1 3.b odd 2 1
855.1.g.a 1 15.d odd 2 1
855.1.g.a 1 57.d even 2 1
855.1.g.a 1 285.b even 2 1
1520.1.m.a 1 4.b odd 2 1
1520.1.m.a 1 20.d odd 2 1
1520.1.m.a 1 76.d even 2 1
1520.1.m.a 1 380.d even 2 1
1805.1.h.a 2 19.c even 3 2
1805.1.h.a 2 19.d odd 6 2
1805.1.h.a 2 95.h odd 6 2
1805.1.h.a 2 95.i even 6 2
1805.1.o.a 6 19.e even 9 6
1805.1.o.a 6 19.f odd 18 6
1805.1.o.a 6 95.o odd 18 6
1805.1.o.a 6 95.p even 18 6

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{1}^{\mathrm{new}}(95, [\chi])\).

Hecke characteristic polynomials

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