Newform orbit 775.1.d.b

• Label: 775.1.d.b
• Level: $775$
• Weight: $1$
• Character orbit: 775.d
• Self dual: yes
• Analytic conductor: $0.387$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -31
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	775.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.386775384791\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 31)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.31.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.120125.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{2} + q^{7} - q^{8} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).

\(n\)	\(251\)	\(652\)
\(\chi(n)\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

526.1

0

1.00000

0

0

0

0

1.00000

−1.00000

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.b	odd	2	1	CM by \(\Q(\sqrt{-31}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	775.1.d.b		1
5.b	even	2	1		31.1.b.a	✓	1
5.c	odd	4	2		775.1.c.a		2
15.d	odd	2	1		279.1.d.b		1
20.d	odd	2	1		496.1.e.a		1
31.b	odd	2	1	CM	775.1.d.b		1
35.c	odd	2	1		1519.1.c.a		1
35.i	odd	6	2		1519.1.n.a		2
35.j	even	6	2		1519.1.n.b		2
40.e	odd	2	1		1984.1.e.b		1
40.f	even	2	1		1984.1.e.a		1
45.h	odd	6	2		2511.1.m.a		2
45.j	even	6	2		2511.1.m.e		2
55.d	odd	2	1		3751.1.d.b		1
55.h	odd	10	4		3751.1.t.a		4
55.j	even	10	4		3751.1.t.c		4
155.c	odd	2	1		31.1.b.a	✓	1
155.f	even	4	2		775.1.c.a		2
155.i	odd	6	2		961.1.e.a		2
155.j	even	6	2		961.1.e.a		2
155.m	odd	10	4		961.1.f.a		4
155.n	even	10	4		961.1.f.a		4
155.u	even	30	8		961.1.h.a		8
155.v	odd	30	8		961.1.h.a		8
465.g	even	2	1		279.1.d.b		1
620.e	even	2	1		496.1.e.a		1
1085.b	even	2	1		1519.1.c.a		1
1085.bh	odd	6	2		1519.1.n.b		2
1085.bn	even	6	2		1519.1.n.a		2
1240.e	odd	2	1		1984.1.e.a		1
1240.o	even	2	1		1984.1.e.b		1
1395.ba	even	6	2		2511.1.m.a		2
1395.bm	odd	6	2		2511.1.m.e		2
1705.h	even	2	1		3751.1.d.b		1
1705.bi	even	10	4		3751.1.t.a		4
1705.cb	odd	10	4		3751.1.t.c		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
31.1.b.a	✓	1	5.b	even	2	1
31.1.b.a	✓	1	155.c	odd	2	1
279.1.d.b		1	15.d	odd	2	1
279.1.d.b		1	465.g	even	2	1
496.1.e.a		1	20.d	odd	2	1
496.1.e.a		1	620.e	even	2	1
775.1.c.a		2	5.c	odd	4	2
775.1.c.a		2	155.f	even	4	2
775.1.d.b		1	1.a	even	1	1	trivial
775.1.d.b		1	31.b	odd	2	1	CM
961.1.e.a		2	155.i	odd	6	2
961.1.e.a		2	155.j	even	6	2
961.1.f.a		4	155.m	odd	10	4
961.1.f.a		4	155.n	even	10	4
961.1.h.a		8	155.u	even	30	8
961.1.h.a		8	155.v	odd	30	8
1519.1.c.a		1	35.c	odd	2	1
1519.1.c.a		1	1085.b	even	2	1
1519.1.n.a		2	35.i	odd	6	2
1519.1.n.a		2	1085.bn	even	6	2
1519.1.n.b		2	35.j	even	6	2
1519.1.n.b		2	1085.bh	odd	6	2
1984.1.e.a		1	40.f	even	2	1
1984.1.e.a		1	1240.e	odd	2	1
1984.1.e.b		1	40.e	odd	2	1
1984.1.e.b		1	1240.o	even	2	1
2511.1.m.a		2	45.h	odd	6	2
2511.1.m.a		2	1395.ba	even	6	2
2511.1.m.e		2	45.j	even	6	2
2511.1.m.e		2	1395.bm	odd	6	2
3751.1.d.b		1	55.d	odd	2	1
3751.1.d.b		1	1705.h	even	2	1
3751.1.t.a		4	55.h	odd	10	4
3751.1.t.a		4	1705.bi	even	10	4
3751.1.t.c		4	55.j	even	10	4
3751.1.t.c		4	1705.cb	odd	10	4

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{1}^{\mathrm{new}}(775, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 1 \)
$3$	\( T \)
$5$	\( T \)
$7$	\( T - 1 \)
$11$	\( T \)