Newform orbit 4704.2.a.t

• Label: 4704.2.a.t
• Level: $4704$
• Weight: $2$
• Character orbit: 4704.a
• Self dual: yes
• Analytic conductor: $37.562$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$4704 = 2^{5} \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4704.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$37.5616291108$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 96)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + q^3 - 2 * q^5 + q^9 - 4 * q^11 + 2 * q^13 - 2 * q^15 + 6 * q^17 - 4 * q^19 - q^25 + q^27 + 2 * q^29 + 4 * q^31 - 4 * q^33 - 2 * q^37 + 2 * q^39 - 2 * q^41 - 4 * q^43 - 2 * q^45 + 8 * q^47 + 6 * q^51 + 10 * q^53 + 8 * q^55 - 4 * q^57 - 4 * q^59 - 6 * q^61 - 4 * q^65 - 4 * q^67 + 16 * q^71 + 6 * q^73 - q^75 - 4 * q^79 + q^81 + 12 * q^83 - 12 * q^85 + 2 * q^87 - 10 * q^89 + 4 * q^93 + 8 * q^95 + 14 * q^97 - 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

0

1.00000

0

−2.00000

0

0

0

1.00000

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	4704.2.a.t		1
4.b	odd	2	1		4704.2.a.e		1
7.b	odd	2	1		96.2.a.a	✓	1
8.b	even	2	1		9408.2.a.bj		1
8.d	odd	2	1		9408.2.a.ct		1
21.c	even	2	1		288.2.a.c		1
28.d	even	2	1		96.2.a.b	yes	1
35.c	odd	2	1		2400.2.a.r		1
35.f	even	4	2		2400.2.f.a		2
56.e	even	2	1		192.2.a.a		1
56.h	odd	2	1		192.2.a.c		1
63.l	odd	6	2		2592.2.i.b		2
63.o	even	6	2		2592.2.i.q		2
84.h	odd	2	1		288.2.a.b		1
105.g	even	2	1		7200.2.a.e		1
105.k	odd	4	2		7200.2.f.x		2
112.j	even	4	2		768.2.d.h		2
112.l	odd	4	2		768.2.d.a		2
140.c	even	2	1		2400.2.a.q		1
140.j	odd	4	2		2400.2.f.r		2
168.e	odd	2	1		576.2.a.g		1
168.i	even	2	1		576.2.a.h		1
252.s	odd	6	2		2592.2.i.w		2
252.bi	even	6	2		2592.2.i.h		2
280.c	odd	2	1		4800.2.a.f		1
280.n	even	2	1		4800.2.a.co		1
280.s	even	4	2		4800.2.f.bh		2
280.y	odd	4	2		4800.2.f.e		2
336.v	odd	4	2		2304.2.d.s		2
336.y	even	4	2		2304.2.d.c		2
420.o	odd	2	1		7200.2.a.bx		1
420.w	even	4	2		7200.2.f.f		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.2.a.a	✓	1	7.b	odd	2	1
96.2.a.b	yes	1	28.d	even	2	1
192.2.a.a		1	56.e	even	2	1
192.2.a.c		1	56.h	odd	2	1
288.2.a.b		1	84.h	odd	2	1
288.2.a.c		1	21.c	even	2	1
576.2.a.g		1	168.e	odd	2	1
576.2.a.h		1	168.i	even	2	1
768.2.d.a		2	112.l	odd	4	2
768.2.d.h		2	112.j	even	4	2
2304.2.d.c		2	336.y	even	4	2
2304.2.d.s		2	336.v	odd	4	2
2400.2.a.q		1	140.c	even	2	1
2400.2.a.r		1	35.c	odd	2	1
2400.2.f.a		2	35.f	even	4	2
2400.2.f.r		2	140.j	odd	4	2
2592.2.i.b		2	63.l	odd	6	2
2592.2.i.h		2	252.bi	even	6	2
2592.2.i.q		2	63.o	even	6	2
2592.2.i.w		2	252.s	odd	6	2
4704.2.a.e		1	4.b	odd	2	1
4704.2.a.t		1	1.a	even	1	1	trivial
4800.2.a.f		1	280.c	odd	2	1
4800.2.a.co		1	280.n	even	2	1
4800.2.f.e		2	280.y	odd	4	2
4800.2.f.bh		2	280.s	even	4	2
7200.2.a.e		1	105.g	even	2	1
7200.2.a.bx		1	420.o	odd	2	1
7200.2.f.f		2	420.w	even	4	2
7200.2.f.x		2	105.k	odd	4	2
9408.2.a.bj		1	8.b	even	2	1
9408.2.a.ct		1	8.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(4704))$:

$T_{5} + 2$

$T_{11} + 4$

$T_{13} - 2$

$T_{19} + 4$

$T_{31} - 4$

Hecke characteristic polynomials

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