Newform orbit 3248.1.k.b

• Label: 3248.1.k.b
• Level: $3248$
• Weight: $1$
• Character orbit: 3248.k
• Self dual: yes
• Analytic conductor: $1.621$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -7, -203, 29
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$3248 = 2^{4} \cdot 7 \cdot 29$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3248.k (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.62096316103$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 203)
Projective image:	$D_{2}$
Projective field:	Galois closure of $\Q(\sqrt{-7}, \sqrt{29})$
Artin image:	$D_4$
Artin field:	Galois closure of 4.0.22736.2
Stark unit:	Root of $x^{4} - 30332x^{3} + 41734x^{2} - 30332x + 1$

$q$-expansion

$f(q)$

$=$

$q + q^{7} - q^{9} + 2 q^{23} + q^{25} - q^{29} + q^{49} + 2 q^{53} - q^{63} + 2 q^{67} - 2 q^{71} + q^{81}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3248\mathbb{Z}\right)^\times$.

$n$	$465$	$785$	$2031$	$2437$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1217.1

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
7.b	odd	2	1	CM by $\Q(\sqrt{-7})$
29.b	even	2	1	RM by $\Q(\sqrt{29})$
203.c	odd	2	1	CM by $\Q(\sqrt{-203})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3248.1.k.b		1
4.b	odd	2	1		203.1.c.a	✓	1
7.b	odd	2	1	CM	3248.1.k.b		1
12.b	even	2	1		1827.1.b.a		1
28.d	even	2	1		203.1.c.a	✓	1
28.f	even	6	2		1421.1.i.a		2
28.g	odd	6	2		1421.1.i.a		2
29.b	even	2	1	RM	3248.1.k.b		1
84.h	odd	2	1		1827.1.b.a		1
116.d	odd	2	1		203.1.c.a	✓	1
203.c	odd	2	1	CM	3248.1.k.b		1
348.b	even	2	1		1827.1.b.a		1
812.c	even	2	1		203.1.c.a	✓	1
812.n	odd	6	2		1421.1.i.a		2
812.s	even	6	2		1421.1.i.a		2
2436.j	odd	2	1		1827.1.b.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
203.1.c.a	✓	1	4.b	odd	2	1
203.1.c.a	✓	1	28.d	even	2	1
203.1.c.a	✓	1	116.d	odd	2	1
203.1.c.a	✓	1	812.c	even	2	1
1421.1.i.a		2	28.f	even	6	2
1421.1.i.a		2	28.g	odd	6	2
1421.1.i.a		2	812.n	odd	6	2
1421.1.i.a		2	812.s	even	6	2
1827.1.b.a		1	12.b	even	2	1
1827.1.b.a		1	84.h	odd	2	1
1827.1.b.a		1	348.b	even	2	1
1827.1.b.a		1	2436.j	odd	2	1
3248.1.k.b		1	1.a	even	1	1	trivial
3248.1.k.b		1	7.b	odd	2	1	CM
3248.1.k.b		1	29.b	even	2	1	RM
3248.1.k.b		1	203.c	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3}$ acting on $S_{1}^{\mathrm{new}}(3248, [\chi])$.

Hecke characteristic polynomials

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