Newform orbit 175.7.d.a

• Label: 175.7.d.a
• Level: $175$
• Weight: $7$
• Character orbit: 175.d
• Self dual: yes
• Analytic conductor: $40.259$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -7
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$175 = 5^{2} \cdot 7$
Weight:	$k$	$=$	$7$
Character orbit:	$[\chi]$	$=$	175.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$40.2594646335$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q - 9 * q^2 + 17 * q^4 + 343 * q^7 + 423 * q^8 + 729 * q^9 + 1962 * q^11 - 3087 * q^14 - 4895 * q^16 - 6561 * q^18 - 17658 * q^22 + 22734 * q^23 + 5831 * q^28 - 21222 * q^29 + 16983 * q^32 + 12393 * q^36 - 101194 * q^37 + 126614 * q^43 + 33354 * q^44 - 204606 * q^46 + 117649 * q^49 - 50346 * q^53 + 145089 * q^56 + 190998 * q^58 + 250047 * q^63 + 160433 * q^64 + 53926 * q^67 - 242478 * q^71 + 308367 * q^72 + 910746 * q^74 + 672966 * q^77 + 929378 * q^79 + 531441 * q^81 - 1139526 * q^86 + 829926 * q^88 + 386478 * q^92 - 1058841 * q^98 + 1430298 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

76.1

0

−9.00000

0

17.0000

0

0

343.000

423.000

729.000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by $\Q(\sqrt{-7})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.7.d.a		1
5.b	even	2	1		7.7.b.a	✓	1
5.c	odd	4	2		175.7.c.a		2
7.b	odd	2	1	CM	175.7.d.a		1
15.d	odd	2	1		63.7.d.a		1
20.d	odd	2	1		112.7.c.a		1
35.c	odd	2	1		7.7.b.a	✓	1
35.f	even	4	2		175.7.c.a		2
35.i	odd	6	2		49.7.d.a		2
35.j	even	6	2		49.7.d.a		2
40.e	odd	2	1		448.7.c.b		1
40.f	even	2	1		448.7.c.a		1
105.g	even	2	1		63.7.d.a		1
140.c	even	2	1		112.7.c.a		1
280.c	odd	2	1		448.7.c.a		1
280.n	even	2	1		448.7.c.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.7.b.a	✓	1	5.b	even	2	1
7.7.b.a	✓	1	35.c	odd	2	1
49.7.d.a		2	35.i	odd	6	2
49.7.d.a		2	35.j	even	6	2
63.7.d.a		1	15.d	odd	2	1
63.7.d.a		1	105.g	even	2	1
112.7.c.a		1	20.d	odd	2	1
112.7.c.a		1	140.c	even	2	1
175.7.c.a		2	5.c	odd	4	2
175.7.c.a		2	35.f	even	4	2
175.7.d.a		1	1.a	even	1	1	trivial
175.7.d.a		1	7.b	odd	2	1	CM
448.7.c.a		1	40.f	even	2	1
448.7.c.a		1	280.c	odd	2	1
448.7.c.b		1	40.e	odd	2	1
448.7.c.b		1	280.n	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 9$ acting on $S_{7}^{\mathrm{new}}(175, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 9$
$3$	$T$
$5$	$T$
$7$	$T - 343$
$11$	$T - 1962$