Newform orbit 252.4.a.d

• Label: 252.4.a.d
• Level: $252$
• Weight: $4$
• Character orbit: 252.a
• Self dual: yes
• Analytic conductor: $14.868$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$252 = 2^{2} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	252.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 28)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 8 * q^5 - 7 * q^7 + 40 * q^11 - 12 * q^13 + 58 * q^17 + 26 * q^19 + 64 * q^23 - 61 * q^25 + 62 * q^29 + 252 * q^31 - 56 * q^35 + 26 * q^37 - 6 * q^41 + 416 * q^43 + 396 * q^47 + 49 * q^49 + 450 * q^53 + 320 * q^55 - 274 * q^59 - 576 * q^61 - 96 * q^65 - 476 * q^67 + 448 * q^71 - 158 * q^73 - 280 * q^77 - 936 * q^79 - 530 * q^83 + 464 * q^85 + 390 * q^89 + 84 * q^91 + 208 * q^95 + 214 * 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

8.00000

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	252.4.a.d		1
3.b	odd	2	1		28.4.a.a	✓	1
4.b	odd	2	1		1008.4.a.o		1
7.b	odd	2	1		1764.4.a.c		1
7.c	even	3	2		1764.4.k.d		2
7.d	odd	6	2		1764.4.k.m		2
12.b	even	2	1		112.4.a.g		1
15.d	odd	2	1		700.4.a.n		1
15.e	even	4	2		700.4.e.a		2
21.c	even	2	1		196.4.a.d		1
21.g	even	6	2		196.4.e.a		2
21.h	odd	6	2		196.4.e.f		2
24.f	even	2	1		448.4.a.a		1
24.h	odd	2	1		448.4.a.p		1
84.h	odd	2	1		784.4.a.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
28.4.a.a	✓	1	3.b	odd	2	1
112.4.a.g		1	12.b	even	2	1
196.4.a.d		1	21.c	even	2	1
196.4.e.a		2	21.g	even	6	2
196.4.e.f		2	21.h	odd	6	2
252.4.a.d		1	1.a	even	1	1	trivial
448.4.a.a		1	24.f	even	2	1
448.4.a.p		1	24.h	odd	2	1
700.4.a.n		1	15.d	odd	2	1
700.4.e.a		2	15.e	even	4	2
784.4.a.a		1	84.h	odd	2	1
1008.4.a.o		1	4.b	odd	2	1
1764.4.a.c		1	7.b	odd	2	1
1764.4.k.d		2	7.c	even	3	2
1764.4.k.m		2	7.d	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(252))$:

$T_{5} - 8$

$T_{11} - 40$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 8$
$7$	$T + 7$
$11$	$T - 40$