Newform orbit 2175.1.h.b

• Label: 2175.1.h.b
• Level: $2175$
• Weight: $1$
• Character orbit: 2175.h
• Self dual: yes
• Analytic conductor: $1.085$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -87
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$2175 = 3 \cdot 5^{2} \cdot 29$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2175.h (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.08546640248$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 87)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.87.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.946125.1
Stark unit:	Root of $x^{6} - 10726x^{5} - 27505x^{4} - 115123540x^{3} - 27505x^{2} - 10726x + 1$

$q$-expansion

$f(q)$

$=$

q + q^2 - q^3 - q^6 + q^7 - q^8 + q^9 - q^11 + q^13 + q^14 - q^16 + q^17 + q^18 - q^21 - q^22 + q^24 + q^26 - q^27 + q^29 + q^33 + q^34 - q^39 + 2 * q^41 - q^42 + q^47 + q^48 - q^51 - q^54 - q^56 + q^58 + q^63 + q^64 + q^66 + q^67 - q^72 - q^77 - q^78 + q^81 + 2 * q^82 - q^87 + q^88 - q^89 + q^91 + q^94 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times$.

$n$	$901$	$1451$	$2002$
$\chi(n)$	$-1$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1826.1

0

1.00000

−1.00000

0

0

−1.00000

1.00000

−1.00000

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
87.d	odd	2	1	CM by $\Q(\sqrt{-87})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2175.1.h.b		1
3.b	odd	2	1		2175.1.h.a		1
5.b	even	2	1		87.1.d.a	✓	1
5.c	odd	4	2		2175.1.b.a		2
15.d	odd	2	1		87.1.d.b	yes	1
15.e	even	4	2		2175.1.b.b		2
20.d	odd	2	1		1392.1.i.a		1
29.b	even	2	1		2175.1.h.a		1
45.h	odd	6	2		2349.1.h.a		2
45.j	even	6	2		2349.1.h.b		2
60.h	even	2	1		1392.1.i.b		1
87.d	odd	2	1	CM	2175.1.h.b		1
145.d	even	2	1		87.1.d.b	yes	1
145.f	odd	4	2		2523.1.b.b		2
145.h	odd	4	2		2175.1.b.b		2
145.l	even	14	6		2523.1.h.a		6
145.n	even	14	6		2523.1.h.b		6
145.s	odd	28	12		2523.1.j.b		12
435.b	odd	2	1		87.1.d.a	✓	1
435.l	even	4	2		2523.1.b.b		2
435.p	even	4	2		2175.1.b.a		2
435.w	odd	14	6		2523.1.h.a		6
435.bb	odd	14	6		2523.1.h.b		6
435.bk	even	28	12		2523.1.j.b		12
580.e	odd	2	1		1392.1.i.b		1
1305.w	even	6	2		2349.1.h.a		2
1305.ba	odd	6	2		2349.1.h.b		2
1740.k	even	2	1		1392.1.i.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
87.1.d.a	✓	1	5.b	even	2	1
87.1.d.a	✓	1	435.b	odd	2	1
87.1.d.b	yes	1	15.d	odd	2	1
87.1.d.b	yes	1	145.d	even	2	1
1392.1.i.a		1	20.d	odd	2	1
1392.1.i.a		1	1740.k	even	2	1
1392.1.i.b		1	60.h	even	2	1
1392.1.i.b		1	580.e	odd	2	1
2175.1.b.a		2	5.c	odd	4	2
2175.1.b.a		2	435.p	even	4	2
2175.1.b.b		2	15.e	even	4	2
2175.1.b.b		2	145.h	odd	4	2
2175.1.h.a		1	3.b	odd	2	1
2175.1.h.a		1	29.b	even	2	1
2175.1.h.b		1	1.a	even	1	1	trivial
2175.1.h.b		1	87.d	odd	2	1	CM
2349.1.h.a		2	45.h	odd	6	2
2349.1.h.a		2	1305.w	even	6	2
2349.1.h.b		2	45.j	even	6	2
2349.1.h.b		2	1305.ba	odd	6	2
2523.1.b.b		2	145.f	odd	4	2
2523.1.b.b		2	435.l	even	4	2
2523.1.h.a		6	145.l	even	14	6
2523.1.h.a		6	435.w	odd	14	6
2523.1.h.b		6	145.n	even	14	6
2523.1.h.b		6	435.bb	odd	14	6
2523.1.j.b		12	145.s	odd	28	12
2523.1.j.b		12	435.bk	even	28	12

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(2175, [\chi])$:

$T_{2} - 1$

$T_{7} - 1$

Hecke characteristic polynomials

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