Newform orbit 5070.2.a.q

• Label: 5070.2.a.q
• Level: $5070$
• Weight: $2$
• Character orbit: 5070.a
• Self dual: yes
• Analytic conductor: $40.484$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	5070.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$40.4841538248$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + q^2 - q^3 + q^4 + q^5 - q^6 - 3 * q^7 + q^8 + q^9 + q^10 + q^11 - q^12 - 3 * q^14 - q^15 + q^16 + q^18 - 5 * q^19 + q^20 + 3 * q^21 + q^22 - 4 * q^23 - q^24 + q^25 - q^27 - 3 * q^28 - q^30 + 10 * q^31 + q^32 - q^33 - 3 * q^35 + q^36 - q^37 - 5 * q^38 + q^40 + 6 * q^41 + 3 * q^42 - 2 * q^43 + q^44 + q^45 - 4 * q^46 - 9 * q^47 - q^48 + 2 * q^49 + q^50 - 13 * q^53 - q^54 + q^55 - 3 * q^56 + 5 * q^57 + 4 * q^59 - q^60 - 2 * q^61 + 10 * q^62 - 3 * q^63 + q^64 - q^66 - 12 * q^67 + 4 * q^69 - 3 * q^70 - 2 * q^71 + q^72 - 16 * q^73 - q^74 - q^75 - 5 * q^76 - 3 * q^77 - 10 * q^79 + q^80 + q^81 + 6 * q^82 + 12 * q^83 + 3 * q^84 - 2 * q^86 + q^88 + q^89 + q^90 - 4 * q^92 - 10 * q^93 - 9 * q^94 - 5 * q^95 - 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

1.00000

−1.00000

1.00000

1.00000

−1.00000

−3.00000

1.00000

1.00000

1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$5$	$-1$
$13$	$+1$

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	5070.2.a.q		1
13.b	even	2	1		5070.2.a.c		1
13.c	even	3	2		390.2.i.b	✓	2
13.d	odd	4	2		5070.2.b.a		2
39.i	odd	6	2		1170.2.i.j		2
65.n	even	6	2		1950.2.i.o		2
65.q	odd	12	4		1950.2.z.i		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
390.2.i.b	✓	2	13.c	even	3	2
1170.2.i.j		2	39.i	odd	6	2
1950.2.i.o		2	65.n	even	6	2
1950.2.z.i		4	65.q	odd	12	4
5070.2.a.c		1	13.b	even	2	1
5070.2.a.q		1	1.a	even	1	1	trivial
5070.2.b.a		2	13.d	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(5070))$:

$T_{7} + 3$

$T_{11} - 1$

$T_{17}$

$T_{31} - 10$

Hecke characteristic polynomials

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