Newform orbit 3724.1.e.d

• Label: 3724.1.e.d
• 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 3.1.3724.2
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.97077232.1
Stark unit:	Root of $x^{6} - 1013956x^{5} + 1000628315x^{4} - 1026107541220x^{3} + 1000628315x^{2} - 1013956x + 1$

$q$-expansion

$f(q)$

$=$

$q + q^{5} + q^{9} + 2 q^{11} + q^{17} - q^{19} - q^{23} - q^{43} + q^{45} - 2 q^{47} + 2 q^{55} - 2 q^{61} - 2 q^{73} + q^{81} + q^{83} + q^{85} - q^{95} + 2 q^{99}+O(q^{100})$

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

1.00000

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

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
532.1.bc.b	✓	2	7.d	odd	6	2
532.1.bc.b	✓	2	133.o	even	6	2
2128.1.cl.b		2	28.f	even	6	2
2128.1.cl.b		2	532.bh	odd	6	2
3724.1.e.b		1	7.b	odd	2	1
3724.1.e.b		1	133.c	even	2	1
3724.1.e.d		1	1.a	even	1	1	trivial
3724.1.e.d		1	19.b	odd	2	1	CM
3724.1.bc.a		2	7.c	even	3	2
3724.1.bc.a		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 $S_{1}^{\mathrm{new}}(3724, [\chi])$:

$T_{5} - 1$

$T_{11} - 2$

Hecke characteristic polynomials

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