Newform orbit 170.2.a.d

• Label: 170.2.a.d
• Level: $170$
• Weight: $2$
• Character orbit: 170.a
• Self dual: yes
• Analytic conductor: $1.357$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$170 = 2 \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	170.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - q^2 + 3 * q^3 + q^4 - q^5 - 3 * q^6 + 2 * q^7 - q^8 + 6 * q^9 + q^10 - 4 * q^11 + 3 * q^12 - 3 * q^13 - 2 * q^14 - 3 * q^15 + q^16 + q^17 - 6 * q^18 + 3 * q^19 - q^20 + 6 * q^21 + 4 * q^22 - 6 * q^23 - 3 * q^24 + q^25 + 3 * q^26 + 9 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^30 - 3 * q^31 - q^32 - 12 * q^33 - q^34 - 2 * q^35 + 6 * q^36 - 8 * q^37 - 3 * q^38 - 9 * q^39 + q^40 - 6 * q^41 - 6 * q^42 + 6 * q^43 - 4 * q^44 - 6 * q^45 + 6 * q^46 - 13 * q^47 + 3 * q^48 - 3 * q^49 - q^50 + 3 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 4 * q^55 - 2 * q^56 + 9 * q^57 - 9 * q^58 + 15 * q^59 - 3 * q^60 + 7 * q^61 + 3 * q^62 + 12 * q^63 + q^64 + 3 * q^65 + 12 * q^66 - 2 * q^67 + q^68 - 18 * q^69 + 2 * q^70 + 9 * q^71 - 6 * q^72 - 3 * q^73 + 8 * q^74 + 3 * q^75 + 3 * q^76 - 8 * q^77 + 9 * q^78 - q^80 + 9 * q^81 + 6 * q^82 + 12 * q^83 + 6 * q^84 - q^85 - 6 * q^86 + 27 * q^87 + 4 * q^88 - 9 * q^89 + 6 * q^90 - 6 * q^91 - 6 * q^92 - 9 * q^93 + 13 * q^94 - 3 * q^95 - 3 * q^96 + 7 * q^97 + 3 * q^98 - 24 * q^99

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

−1.00000

3.00000

1.00000

−1.00000

−3.00000

2.00000

−1.00000

6.00000

1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$5$	$+1$
$17$	$-1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	170.2.a.d	✓	1
3.b	odd	2	1		1530.2.a.o		1
4.b	odd	2	1		1360.2.a.a		1
5.b	even	2	1		850.2.a.f		1
5.c	odd	4	2		850.2.c.a		2
7.b	odd	2	1		8330.2.a.a		1
8.b	even	2	1		5440.2.a.b		1
8.d	odd	2	1		5440.2.a.y		1
15.d	odd	2	1		7650.2.a.l		1
17.b	even	2	1		2890.2.a.b		1
17.c	even	4	2		2890.2.b.d		2
20.d	odd	2	1		6800.2.a.z		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
170.2.a.d	✓	1	1.a	even	1	1	trivial
850.2.a.f		1	5.b	even	2	1
850.2.c.a		2	5.c	odd	4	2
1360.2.a.a		1	4.b	odd	2	1
1530.2.a.o		1	3.b	odd	2	1
2890.2.a.b		1	17.b	even	2	1
2890.2.b.d		2	17.c	even	4	2
5440.2.a.b		1	8.b	even	2	1
5440.2.a.y		1	8.d	odd	2	1
6800.2.a.z		1	20.d	odd	2	1
7650.2.a.l		1	15.d	odd	2	1
8330.2.a.a		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(170))$:

$T_{3} - 3$

$T_{7} - 2$

$T_{13} + 3$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$
$3$	$T - 3$
$5$	$T + 1$
$7$	$T - 2$
$11$	$T + 4$