Newform orbit 510.2.a.b

• Label: 510.2.a.b
• Level: $510$
• Weight: $2$
• Character orbit: 510.a
• Self dual: yes
• Analytic conductor: $4.072$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$510 = 2 \cdot 3 \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	510.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$4.07237050309$
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 + q^3 + q^4 + q^5 - q^6 - 2 * q^7 - q^8 + q^9 - q^10 + 4 * q^11 + q^12 + 2 * q^14 + q^15 + q^16 + q^17 - q^18 + 4 * q^19 + q^20 - 2 * q^21 - 4 * q^22 + 4 * q^23 - q^24 + q^25 + q^27 - 2 * q^28 + 6 * q^29 - q^30 - 8 * q^31 - q^32 + 4 * q^33 - q^34 - 2 * q^35 + q^36 - 6 * q^37 - 4 * q^38 - q^40 + 8 * q^41 + 2 * q^42 + 2 * q^43 + 4 * q^44 + q^45 - 4 * q^46 - 8 * q^47 + q^48 - 3 * q^49 - q^50 + q^51 + 14 * q^53 - q^54 + 4 * q^55 + 2 * q^56 + 4 * q^57 - 6 * q^58 + 6 * q^59 + q^60 + 2 * q^61 + 8 * q^62 - 2 * q^63 + q^64 - 4 * q^66 + 2 * q^67 + q^68 + 4 * q^69 + 2 * q^70 - 10 * q^71 - q^72 + 4 * q^73 + 6 * q^74 + q^75 + 4 * q^76 - 8 * q^77 + 4 * q^79 + q^80 + q^81 - 8 * q^82 - 16 * q^83 - 2 * q^84 + q^85 - 2 * q^86 + 6 * q^87 - 4 * q^88 + 6 * q^89 - q^90 + 4 * q^92 - 8 * q^93 + 8 * q^94 + 4 * q^95 - q^96 - 8 * q^97 + 3 * q^98 + 4 * 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

−2.00000

−1.00000

1.00000

−1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$5$	$-1$
$17$	$-1$

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	510.2.a.b	✓	1
3.b	odd	2	1		1530.2.a.i		1
4.b	odd	2	1		4080.2.a.n		1
5.b	even	2	1		2550.2.a.y		1
5.c	odd	4	2		2550.2.d.j		2
15.d	odd	2	1		7650.2.a.y		1
17.b	even	2	1		8670.2.a.c		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
510.2.a.b	✓	1	1.a	even	1	1	trivial
1530.2.a.i		1	3.b	odd	2	1
2550.2.a.y		1	5.b	even	2	1
2550.2.d.j		2	5.c	odd	4	2
4080.2.a.n		1	4.b	odd	2	1
7650.2.a.y		1	15.d	odd	2	1
8670.2.a.c		1	17.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 $S_{2}^{\mathrm{new}}(\Gamma_0(510))$:

$T_{7} + 2$

$T_{11} - 4$

$T_{13}$

Hecke characteristic polynomials

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