Newform orbit 504.4.a.c

• Label: 504.4.a.c
• Level: $504$
• Weight: $4$
• Character orbit: 504.a
• Self dual: yes
• Analytic conductor: $29.737$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$504 = 2^{3} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	504.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$29.7369626429$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 168)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 2 * q^5 - 7 * q^7 - 52 * q^11 + 86 * q^13 + 30 * q^17 - 4 * q^19 - 120 * q^23 - 121 * q^25 - 246 * q^29 + 80 * q^31 - 14 * q^35 - 290 * q^37 + 374 * q^41 + 164 * q^43 - 464 * q^47 + 49 * q^49 + 162 * q^53 - 104 * q^55 - 180 * q^59 - 666 * q^61 + 172 * q^65 - 628 * q^67 - 296 * q^71 - 518 * q^73 + 364 * q^77 - 1184 * q^79 - 220 * q^83 + 60 * q^85 + 774 * q^89 - 602 * q^91 - 8 * q^95 - 1086 * q^97

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

0

0

2.00000

0

−7.00000

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$
$7$	$+1$

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	504.4.a.c		1
3.b	odd	2	1		168.4.a.f	✓	1
4.b	odd	2	1		1008.4.a.l		1
12.b	even	2	1		336.4.a.c		1
21.c	even	2	1		1176.4.a.e		1
24.f	even	2	1		1344.4.a.v		1
24.h	odd	2	1		1344.4.a.g		1
84.h	odd	2	1		2352.4.a.bb		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
168.4.a.f	✓	1	3.b	odd	2	1
336.4.a.c		1	12.b	even	2	1
504.4.a.c		1	1.a	even	1	1	trivial
1008.4.a.l		1	4.b	odd	2	1
1176.4.a.e		1	21.c	even	2	1
1344.4.a.g		1	24.h	odd	2	1
1344.4.a.v		1	24.f	even	2	1
2352.4.a.bb		1	84.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(504))$:

$T_{5} - 2$

$T_{11} + 52$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 2$
$7$	$T + 7$
$11$	$T + 52$