Newform orbit 1062.6.a.a

• Label: 1062.6.a.a
• Level: $1062$
• Weight: $6$
• Character orbit: 1062.a
• Self dual: yes
• Analytic conductor: $170.328$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1062 = 2 \cdot 3^{2} \cdot 59$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	1062.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$170.327616641$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 354)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 4 * q^2 + 16 * q^4 - 10 * q^5 + 144 * q^7 - 64 * q^8 + 40 * q^10 - 668 * q^11 - 270 * q^13 - 576 * q^14 + 256 * q^16 + 758 * q^17 + 868 * q^19 - 160 * q^20 + 2672 * q^22 - 784 * q^23 - 3025 * q^25 + 1080 * q^26 + 2304 * q^28 + 4574 * q^29 + 8948 * q^31 - 1024 * q^32 - 3032 * q^34 - 1440 * q^35 - 670 * q^37 - 3472 * q^38 + 640 * q^40 + 7934 * q^41 + 4884 * q^43 - 10688 * q^44 + 3136 * q^46 - 24280 * q^47 + 3929 * q^49 + 12100 * q^50 - 4320 * q^52 - 28962 * q^53 + 6680 * q^55 - 9216 * q^56 - 18296 * q^58 + 3481 * q^59 + 30490 * q^61 - 35792 * q^62 + 4096 * q^64 + 2700 * q^65 - 30764 * q^67 + 12128 * q^68 + 5760 * q^70 - 22452 * q^71 - 20966 * q^73 + 2680 * q^74 + 13888 * q^76 - 96192 * q^77 + 70520 * q^79 - 2560 * q^80 - 31736 * q^82 - 29756 * q^83 - 7580 * q^85 - 19536 * q^86 + 42752 * q^88 + 16470 * q^89 - 38880 * q^91 - 12544 * q^92 + 97120 * q^94 - 8680 * q^95 + 18506 * q^97 - 15716 * q^98

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

−4.00000

0

16.0000

−10.0000

0

144.000

−64.0000

0

40.0000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$59$	$-1$

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	1062.6.a.a		1
3.b	odd	2	1		354.6.a.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
354.6.a.a	✓	1	3.b	odd	2	1
1062.6.a.a		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{5} + 10$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(1062))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 4$
$3$	$T$
$5$	$T + 10$
$7$	$T - 144$
$11$	$T + 668$