Newform orbit 95.1.d.b

• Label: 95.1.d.b
• Level: $95$
• Weight: $1$
• Character orbit: 95.d
• Self dual: yes
• Analytic conductor: $0.047$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{4}$
• CM discriminant: -95
• Inner twists: $4$

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:	\(2\)
Coefficient field:	\(\Q(\sqrt{2}) \)
Defining polynomial:	\( x^{2} - 2 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{4}\)
Projective field:	Galois closure of 4.2.475.1
Artin image:	$D_8$
Artin field:	Galois closure of 8.2.4286875.1

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - \beta q^{2} + \beta q^{3} + q^{4} - q^{5} - 2 q^{6} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \)

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

1.41421
−1.41421

−1.41421

1.41421

1.00000

−1.00000

−2.00000

0

0

1.00000

1.41421

94.2

1.41421

−1.41421

1.00000

−1.00000

−2.00000

0

0

1.00000

−1.41421

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.1.d.b	✓	2
3.b	odd	2	1		855.1.g.c		2
4.b	odd	2	1		1520.1.m.b		2
5.b	even	2	1	inner	95.1.d.b	✓	2
5.c	odd	4	2		475.1.c.b		2
15.d	odd	2	1		855.1.g.c		2
19.b	odd	2	1	inner	95.1.d.b	✓	2
19.c	even	3	2		1805.1.h.b		4
19.d	odd	6	2		1805.1.h.b		4
19.e	even	9	6		1805.1.o.b		12
19.f	odd	18	6		1805.1.o.b		12
20.d	odd	2	1		1520.1.m.b		2
57.d	even	2	1		855.1.g.c		2
76.d	even	2	1		1520.1.m.b		2
95.d	odd	2	1	CM	95.1.d.b	✓	2
95.g	even	4	2		475.1.c.b		2
95.h	odd	6	2		1805.1.h.b		4
95.i	even	6	2		1805.1.h.b		4
95.o	odd	18	6		1805.1.o.b		12
95.p	even	18	6		1805.1.o.b		12
285.b	even	2	1		855.1.g.c		2
380.d	even	2	1		1520.1.m.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.1.d.b	✓	2	1.a	even	1	1	trivial
95.1.d.b	✓	2	5.b	even	2	1	inner
95.1.d.b	✓	2	19.b	odd	2	1	inner
95.1.d.b	✓	2	95.d	odd	2	1	CM
475.1.c.b		2	5.c	odd	4	2
475.1.c.b		2	95.g	even	4	2
855.1.g.c		2	3.b	odd	2	1
855.1.g.c		2	15.d	odd	2	1
855.1.g.c		2	57.d	even	2	1
855.1.g.c		2	285.b	even	2	1
1520.1.m.b		2	4.b	odd	2	1
1520.1.m.b		2	20.d	odd	2	1
1520.1.m.b		2	76.d	even	2	1
1520.1.m.b		2	380.d	even	2	1
1805.1.h.b		4	19.c	even	3	2
1805.1.h.b		4	19.d	odd	6	2
1805.1.h.b		4	95.h	odd	6	2
1805.1.h.b		4	95.i	even	6	2
1805.1.o.b		12	19.e	even	9	6
1805.1.o.b		12	19.f	odd	18	6
1805.1.o.b		12	95.o	odd	18	6
1805.1.o.b		12	95.p	even	18	6

Hecke kernels

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

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} - 2 \)
$3$	\( T^{2} - 2 \)
$5$	\( (T + 1)^{2} \)
$7$	\( T^{2} \)
$11$	\( T^{2} \)