Newform orbit 490.4.a.g

• Label: 490.4.a.g
• Level: $490$
• Weight: $4$
• Character orbit: 490.a
• Self dual: yes
• Analytic conductor: $28.911$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$490 = 2 \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	490.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 2 * q^2 + 8 * q^3 + 4 * q^4 + 5 * q^5 - 16 * q^6 - 8 * q^8 + 37 * q^9 - 10 * q^10 + 68 * q^11 + 32 * q^12 - 34 * q^13 + 40 * q^15 + 16 * q^16 - 74 * q^17 - 74 * q^18 + 128 * q^19 + 20 * q^20 - 136 * q^22 - 80 * q^23 - 64 * q^24 + 25 * q^25 + 68 * q^26 + 80 * q^27 + 286 * q^29 - 80 * q^30 + 24 * q^31 - 32 * q^32 + 544 * q^33 + 148 * q^34 + 148 * q^36 + 294 * q^37 - 256 * q^38 - 272 * q^39 - 40 * q^40 - 66 * q^41 - 124 * q^43 + 272 * q^44 + 185 * q^45 + 160 * q^46 - 312 * q^47 + 128 * q^48 - 50 * q^50 - 592 * q^51 - 136 * q^52 - 34 * q^53 - 160 * q^54 + 340 * q^55 + 1024 * q^57 - 572 * q^58 - 168 * q^59 + 160 * q^60 - 170 * q^61 - 48 * q^62 + 64 * q^64 - 170 * q^65 - 1088 * q^66 + 564 * q^67 - 296 * q^68 - 640 * q^69 + 616 * q^71 - 296 * q^72 - 250 * q^73 - 588 * q^74 + 200 * q^75 + 512 * q^76 + 544 * q^78 - 944 * q^79 + 80 * q^80 - 359 * q^81 + 132 * q^82 - 672 * q^83 - 370 * q^85 + 248 * q^86 + 2288 * q^87 - 544 * q^88 + 1430 * q^89 - 370 * q^90 - 320 * q^92 + 192 * q^93 + 624 * q^94 + 640 * q^95 - 256 * q^96 + 1270 * q^97 + 2516 * 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

8.00000

4.00000

5.00000

−16.0000

0

−8.00000

37.0000

−10.0000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$5$	$-1$
$7$	$-1$

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	490.4.a.g		1
5.b	even	2	1		2450.4.a.x		1
7.b	odd	2	1		70.4.a.a	✓	1
7.c	even	3	2		490.4.e.j		2
7.d	odd	6	2		490.4.e.r		2
21.c	even	2	1		630.4.a.s		1
28.d	even	2	1		560.4.a.q		1
35.c	odd	2	1		350.4.a.v		1
35.f	even	4	2		350.4.c.n		2
56.e	even	2	1		2240.4.a.d		1
56.h	odd	2	1		2240.4.a.bi		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.a.a	✓	1	7.b	odd	2	1
350.4.a.v		1	35.c	odd	2	1
350.4.c.n		2	35.f	even	4	2
490.4.a.g		1	1.a	even	1	1	trivial
490.4.e.j		2	7.c	even	3	2
490.4.e.r		2	7.d	odd	6	2
560.4.a.q		1	28.d	even	2	1
630.4.a.s		1	21.c	even	2	1
2240.4.a.d		1	56.e	even	2	1
2240.4.a.bi		1	56.h	odd	2	1
2450.4.a.x		1	5.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 $S_{4}^{\mathrm{new}}(\Gamma_0(490))$:

$T_{3} - 8$

$T_{11} - 68$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$
$3$	$T - 8$
$5$	$T - 5$
$7$	$T$
$11$	$T - 68$