Newform orbit 3724.1.e.a

• Label: 3724.1.e.a
• Level: $3724$
• Weight: $1$
• Character orbit: 3724.e
• Self dual: yes
• Analytic conductor: $1.859$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -19
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3724.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.85851810705\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 532)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.3724.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.97077232.2

$q$-expansion

\(f(q)\)

\(=\)

\( q - 2 q^{5} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3724\mathbb{Z}\right)^\times\).

\(n\)	\(1863\)	\(3041\)	\(3137\)
\(\chi(n)\)	\(1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1177.1

0

0

0

0

−2.00000

0

0

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	3724.1.e.a		1
7.b	odd	2	1		3724.1.e.e		1
7.c	even	3	2		3724.1.bc.d		2
7.d	odd	6	2		532.1.bc.a	✓	2
19.b	odd	2	1	CM	3724.1.e.a		1
28.f	even	6	2		2128.1.cl.a		2
133.c	even	2	1		3724.1.e.e		1
133.o	even	6	2		532.1.bc.a	✓	2
133.r	odd	6	2		3724.1.bc.d		2
532.bh	odd	6	2		2128.1.cl.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
532.1.bc.a	✓	2	7.d	odd	6	2
532.1.bc.a	✓	2	133.o	even	6	2
2128.1.cl.a		2	28.f	even	6	2
2128.1.cl.a		2	532.bh	odd	6	2
3724.1.e.a		1	1.a	even	1	1	trivial
3724.1.e.a		1	19.b	odd	2	1	CM
3724.1.e.e		1	7.b	odd	2	1
3724.1.e.e		1	133.c	even	2	1
3724.1.bc.d		2	7.c	even	3	2
3724.1.bc.d		2	133.r	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(3724, [\chi])\):

\( T_{5} + 2 \)

\( T_{11} + 1 \)

Hecke characteristic polynomials

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