Newform orbit 175.5.d.b

• Label: 175.5.d.b
• Level: $175$
• Weight: $5$
• Character orbit: 175.d
• Self dual: yes
• Analytic conductor: $18.090$
• Analytic rank: $0$
• Dimension: $2$
• CM discriminant: -7
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21})$
Defining polynomial:	$x^{2} - x - 5$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$3$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \frac{1}{2}(1 + 3\sqrt{21})$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q - b * q^2 + (b + 31) * q^4 + 49 * q^7 + (-16*b - 47) * q^8 + 81 * q^9 + (16*b + 95) * q^11 - 49*b * q^14 + (47*b + 256) * q^16 - 81*b * q^18 + (-111*b - 752) * q^22 + (-96*b + 415) * q^23 + (49*b + 1519) * q^28 + (-144*b - 545) * q^29 + (-47*b - 1457) * q^32 + (81*b + 2511) * q^36 + (304*b + 495) * q^37 + (464*b - 65) * q^43 + (607*b + 3697) * q^44 + (-319*b + 4512) * q^46 + 2401 * q^49 - 5582 * q^53 + (-784*b - 2303) * q^56 + (689*b + 6768) * q^58 + 3969 * q^63 + (752*b - 1887) * q^64 + (944*b - 2945) * q^67 + (1216*b - 2065) * q^71 + (-1296*b - 3807) * q^72 + (-799*b - 14288) * q^74 + (784*b + 4655) * q^77 + (-1504*b + 2575) * q^79 + 6561 * q^81 + (-399*b - 21808) * q^86 + (-2528*b - 16497) * q^88 + (-2657*b + 8353) * q^92 - 2401*b * q^98 + (1296*b + 7695) * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q - q^2 + 63 * q^4 + 98 * q^7 - 110 * q^8 + 162 * q^9 + 206 * q^11 - 49 * q^14 + 559 * q^16 - 81 * q^18 - 1615 * q^22 + 734 * q^23 + 3087 * q^28 - 1234 * q^29 - 2961 * q^32 + 5103 * q^36 + 1294 * q^37 + 334 * q^43 + 8001 * q^44 + 8705 * q^46 + 4802 * q^49 - 11164 * q^53 - 5390 * q^56 + 14225 * q^58 + 7938 * q^63 - 3022 * q^64 - 4946 * q^67 - 2914 * q^71 - 8910 * q^72 - 29375 * q^74 + 10094 * q^77 + 3646 * q^79 + 13122 * q^81 - 44015 * q^86 - 35522 * q^88 + 14049 * q^92 - 2401 * q^98 + 16686 * 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

2.79129
−1.79129

−7.37386

0

38.3739

0

0

49.0000

−164.982

81.0000

0

76.2

6.37386

0

24.6261

0

0

49.0000

54.9818

81.0000

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	175.5.d.b	✓	2
5.b	even	2	1		175.5.d.d	yes	2
5.c	odd	4	2		175.5.c.b		4
7.b	odd	2	1	CM	175.5.d.b	✓	2
35.c	odd	2	1		175.5.d.d	yes	2
35.f	even	4	2		175.5.c.b		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
175.5.c.b		4	5.c	odd	4	2
175.5.c.b		4	35.f	even	4	2
175.5.d.b	✓	2	1.a	even	1	1	trivial
175.5.d.b	✓	2	7.b	odd	2	1	CM
175.5.d.d	yes	2	5.b	even	2	1
175.5.d.d	yes	2	35.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{2} + T_{2} - 47$ acting on $S_{5}^{\mathrm{new}}(175, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2} + T - 47$
$3$	$T^{2}$
$5$	$T^{2}$
$7$	$(T - 49)^{2}$
$11$	$T^{2} - 206T - 1487$