Newform orbit 49.4.a.d

• Label: 49.4.a.d
• Level: $49$
• Weight: $4$
• Character orbit: 49.a
• Self dual: yes
• Analytic conductor: $2.891$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$49 = 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 2 * q^2 + 7 * q^3 - 4 * q^4 + 7 * q^5 + 14 * q^6 - 24 * q^8 + 22 * q^9 + 14 * q^10 - 5 * q^11 - 28 * q^12 - 14 * q^13 + 49 * q^15 - 16 * q^16 - 21 * q^17 + 44 * q^18 + 49 * q^19 - 28 * q^20 - 10 * q^22 - 159 * q^23 - 168 * q^24 - 76 * q^25 - 28 * q^26 - 35 * q^27 + 58 * q^29 + 98 * q^30 + 147 * q^31 + 160 * q^32 - 35 * q^33 - 42 * q^34 - 88 * q^36 + 219 * q^37 + 98 * q^38 - 98 * q^39 - 168 * q^40 + 350 * q^41 - 124 * q^43 + 20 * q^44 + 154 * q^45 - 318 * q^46 + 525 * q^47 - 112 * q^48 - 152 * q^50 - 147 * q^51 + 56 * q^52 + 303 * q^53 - 70 * q^54 - 35 * q^55 + 343 * q^57 + 116 * q^58 - 105 * q^59 - 196 * q^60 - 413 * q^61 + 294 * q^62 + 448 * q^64 - 98 * q^65 - 70 * q^66 + 415 * q^67 + 84 * q^68 - 1113 * q^69 - 432 * q^71 - 528 * q^72 - 1113 * q^73 + 438 * q^74 - 532 * q^75 - 196 * q^76 - 196 * q^78 - 103 * q^79 - 112 * q^80 - 839 * q^81 + 700 * q^82 + 1092 * q^83 - 147 * q^85 - 248 * q^86 + 406 * q^87 + 120 * q^88 - 329 * q^89 + 308 * q^90 + 636 * q^92 + 1029 * q^93 + 1050 * q^94 + 343 * q^95 + 1120 * q^96 - 882 * q^97 - 110 * 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

2.00000

7.00000

−4.00000

7.00000

14.0000

0

−24.0000

22.0000

14.0000

Atkin-Lehner signs

$p$	Sign
$7$	$+1$

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	49.4.a.d		1
3.b	odd	2	1		441.4.a.d		1
4.b	odd	2	1		784.4.a.b		1
5.b	even	2	1		1225.4.a.c		1
7.b	odd	2	1		49.4.a.c		1
7.c	even	3	2		7.4.c.a	✓	2
7.d	odd	6	2		49.4.c.a		2
21.c	even	2	1		441.4.a.e		1
21.g	even	6	2		441.4.e.k		2
21.h	odd	6	2		63.4.e.b		2
28.d	even	2	1		784.4.a.r		1
28.g	odd	6	2		112.4.i.c		2
35.c	odd	2	1		1225.4.a.d		1
35.j	even	6	2		175.4.e.a		2
35.l	odd	12	4		175.4.k.a		4
56.k	odd	6	2		448.4.i.a		2
56.p	even	6	2		448.4.i.f		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.4.c.a	✓	2	7.c	even	3	2
49.4.a.c		1	7.b	odd	2	1
49.4.a.d		1	1.a	even	1	1	trivial
49.4.c.a		2	7.d	odd	6	2
63.4.e.b		2	21.h	odd	6	2
112.4.i.c		2	28.g	odd	6	2
175.4.e.a		2	35.j	even	6	2
175.4.k.a		4	35.l	odd	12	4
441.4.a.d		1	3.b	odd	2	1
441.4.a.e		1	21.c	even	2	1
441.4.e.k		2	21.g	even	6	2
448.4.i.a		2	56.k	odd	6	2
448.4.i.f		2	56.p	even	6	2
784.4.a.b		1	4.b	odd	2	1
784.4.a.r		1	28.d	even	2	1
1225.4.a.c		1	5.b	even	2	1
1225.4.a.d		1	35.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(49))$:

$T_{2} - 2$

$T_{3} - 7$

Hecke characteristic polynomials

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