Newform orbit 357.2.a.c

• Label: 357.2.a.c
• Level: $357$
• Weight: $2$
• Character orbit: 357.a
• Self dual: yes
• Analytic conductor: $2.851$
• Analytic rank: $1$
• 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:	$1$
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^3 - 2 * q^4 + q^5 + q^7 + q^9 - 5 * q^11 + 2 * q^12 - 5 * q^13 - q^15 + 4 * q^16 + q^17 - 5 * q^19 - 2 * q^20 - q^21 - q^23 - 4 * q^25 - q^27 - 2 * q^28 - 6 * q^29 - 6 * q^31 + 5 * q^33 + q^35 - 2 * q^36 + 4 * q^37 + 5 * q^39 + 7 * q^41 - 7 * q^43 + 10 * q^44 + q^45 + 6 * q^47 - 4 * q^48 + q^49 - q^51 + 10 * q^52 + 6 * q^53 - 5 * q^55 + 5 * q^57 + 14 * q^59 + 2 * q^60 + q^63 - 8 * q^64 - 5 * q^65 - 12 * q^67 - 2 * q^68 + q^69 + 4 * q^71 + 6 * q^73 + 4 * q^75 + 10 * q^76 - 5 * q^77 - 6 * q^79 + 4 * q^80 + q^81 - 6 * q^83 + 2 * q^84 + q^85 + 6 * q^87 + 12 * q^89 - 5 * q^91 + 2 * q^92 + 6 * q^93 - 5 * q^95 + 8 * q^97 - 5 * 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

0

−1.00000

−2.00000

1.00000

0

1.00000

0

1.00000

0

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.c	✓	1
3.b	odd	2	1		1071.2.a.c		1
4.b	odd	2	1		5712.2.a.u		1
5.b	even	2	1		8925.2.a.o		1
7.b	odd	2	1		2499.2.a.g		1
17.b	even	2	1		6069.2.a.c		1
21.c	even	2	1		7497.2.a.i		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
357.2.a.c	✓	1	1.a	even	1	1	trivial
1071.2.a.c		1	3.b	odd	2	1
2499.2.a.g		1	7.b	odd	2	1
5712.2.a.u		1	4.b	odd	2	1
6069.2.a.c		1	17.b	even	2	1
7497.2.a.i		1	21.c	even	2	1
8925.2.a.o		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 $S_{2}^{\mathrm{new}}(\Gamma_0(357))$:

$T_{2}$

$T_{11} + 5$

Hecke characteristic polynomials

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