Newform orbit 1900.1.e.a

• Label: 1900.1.e.a
• Level: $1900$
• Weight: $1$
• Character orbit: 1900.e
• Self dual: yes
• Analytic conductor: $0.948$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -19
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1900.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.948223524003\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 76)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.76.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.722000.1

$q$-expansion

\(f(q)\)

\(=\)

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\)	\(77\)	\(401\)	\(951\)
\(\chi(n)\)	\(1\)	\(-1\)	\(1\)

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

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1101.1

0

0

0

0

0

0

1.00000

0

1.00000

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1900.1.e.a		1
5.b	even	2	1		76.1.c.a	✓	1
5.c	odd	4	2		1900.1.g.a		2
15.d	odd	2	1		684.1.h.a		1
19.b	odd	2	1	CM	1900.1.e.a		1
20.d	odd	2	1		304.1.e.a		1
35.c	odd	2	1		3724.1.e.c		1
35.i	odd	6	2		3724.1.bc.b		2
35.j	even	6	2		3724.1.bc.c		2
40.e	odd	2	1		1216.1.e.b		1
40.f	even	2	1		1216.1.e.a		1
60.h	even	2	1		2736.1.o.b		1
95.d	odd	2	1		76.1.c.a	✓	1
95.g	even	4	2		1900.1.g.a		2
95.h	odd	6	2		1444.1.h.a		2
95.i	even	6	2		1444.1.h.a		2
95.o	odd	18	6		1444.1.j.a		6
95.p	even	18	6		1444.1.j.a		6
285.b	even	2	1		684.1.h.a		1
380.d	even	2	1		304.1.e.a		1
665.g	even	2	1		3724.1.e.c		1
665.x	odd	6	2		3724.1.bc.c		2
665.y	even	6	2		3724.1.bc.b		2
760.b	odd	2	1		1216.1.e.a		1
760.p	even	2	1		1216.1.e.b		1
1140.p	odd	2	1		2736.1.o.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
76.1.c.a	✓	1	5.b	even	2	1
76.1.c.a	✓	1	95.d	odd	2	1
304.1.e.a		1	20.d	odd	2	1
304.1.e.a		1	380.d	even	2	1
684.1.h.a		1	15.d	odd	2	1
684.1.h.a		1	285.b	even	2	1
1216.1.e.a		1	40.f	even	2	1
1216.1.e.a		1	760.b	odd	2	1
1216.1.e.b		1	40.e	odd	2	1
1216.1.e.b		1	760.p	even	2	1
1444.1.h.a		2	95.h	odd	6	2
1444.1.h.a		2	95.i	even	6	2
1444.1.j.a		6	95.o	odd	18	6
1444.1.j.a		6	95.p	even	18	6
1900.1.e.a		1	1.a	even	1	1	trivial
1900.1.e.a		1	19.b	odd	2	1	CM
1900.1.g.a		2	5.c	odd	4	2
1900.1.g.a		2	95.g	even	4	2
2736.1.o.b		1	60.h	even	2	1
2736.1.o.b		1	1140.p	odd	2	1
3724.1.e.c		1	35.c	odd	2	1
3724.1.e.c		1	665.g	even	2	1
3724.1.bc.b		2	35.i	odd	6	2
3724.1.bc.b		2	665.y	even	6	2
3724.1.bc.c		2	35.j	even	6	2
3724.1.bc.c		2	665.x	odd	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} - 1 \) acting on \(S_{1}^{\mathrm{new}}(1900, [\chi])\).

Hecke characteristic polynomials

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