Newform orbit 357.2.a.d

• Label: 357.2.a.d
• Level: $357$
• Weight: $2$
• Character orbit: 357.a
• Self dual: yes
• Analytic conductor: $2.851$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$2.85065935216$
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 + 2 * q^2 + q^3 + 2 * q^4 + q^5 + 2 * q^6 - q^7 + q^9 + 2 * q^10 + q^11 + 2 * q^12 + q^13 - 2 * q^14 + q^15 - 4 * q^16 - q^17 + 2 * q^18 + q^19 + 2 * q^20 - q^21 + 2 * q^22 - 3 * q^23 - 4 * q^25 + 2 * q^26 + q^27 - 2 * q^28 - 2 * q^29 + 2 * q^30 - 8 * q^32 + q^33 - 2 * q^34 - q^35 + 2 * q^36 - 6 * q^37 + 2 * q^38 + q^39 - q^41 - 2 * q^42 + 5 * q^43 + 2 * q^44 + q^45 - 6 * q^46 + 12 * q^47 - 4 * q^48 + q^49 - 8 * q^50 - q^51 + 2 * q^52 + 2 * q^54 + q^55 + q^57 - 4 * q^58 + 2 * q^60 - 2 * q^61 - q^63 - 8 * q^64 + q^65 + 2 * q^66 - 8 * q^67 - 2 * q^68 - 3 * q^69 - 2 * q^70 + 6 * q^73 - 12 * q^74 - 4 * q^75 + 2 * q^76 - q^77 + 2 * q^78 - 4 * q^79 - 4 * q^80 + q^81 - 2 * q^82 + 6 * q^83 - 2 * q^84 - q^85 + 10 * q^86 - 2 * q^87 + 16 * q^89 + 2 * q^90 - q^91 - 6 * q^92 + 24 * q^94 + q^95 - 8 * q^96 - 12 * q^97 + 2 * q^98 + 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

2.00000

1.00000

2.00000

1.00000

2.00000

−1.00000

0

1.00000

2.00000

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$7$	$+1$
$17$	$+1$

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	357.2.a.d	✓	1
3.b	odd	2	1		1071.2.a.a		1
4.b	odd	2	1		5712.2.a.i		1
5.b	even	2	1		8925.2.a.a		1
7.b	odd	2	1		2499.2.a.m		1
17.b	even	2	1		6069.2.a.e		1
21.c	even	2	1		7497.2.a.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
357.2.a.d	✓	1	1.a	even	1	1	trivial
1071.2.a.a		1	3.b	odd	2	1
2499.2.a.m		1	7.b	odd	2	1
5712.2.a.i		1	4.b	odd	2	1
6069.2.a.e		1	17.b	even	2	1
7497.2.a.b		1	21.c	even	2	1
8925.2.a.a		1	5.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(357))$:

$T_{2} - 2$

$T_{11} - 1$

Hecke characteristic polynomials

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