Newform orbit 490.4.a.f

• Label: 490.4.a.f
• Level: $490$
• Weight: $4$
• Character orbit: 490.a
• Self dual: yes
• Analytic conductor: $28.911$
• Analytic rank: $1$
• 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:	$1$
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 + 3 * q^3 + 4 * q^4 - 5 * q^5 - 6 * q^6 - 8 * q^8 - 18 * q^9 + 10 * q^10 - 17 * q^11 + 12 * q^12 + 81 * q^13 - 15 * q^15 + 16 * q^16 + 91 * q^17 + 36 * q^18 - 102 * q^19 - 20 * q^20 + 34 * q^22 - 90 * q^23 - 24 * q^24 + 25 * q^25 - 162 * q^26 - 135 * q^27 - 129 * q^29 + 30 * q^30 - 116 * q^31 - 32 * q^32 - 51 * q^33 - 182 * q^34 - 72 * q^36 + 314 * q^37 + 204 * q^38 + 243 * q^39 + 40 * q^40 + 124 * q^41 - 434 * q^43 - 68 * q^44 + 90 * q^45 + 180 * q^46 - 497 * q^47 + 48 * q^48 - 50 * q^50 + 273 * q^51 + 324 * q^52 - 584 * q^53 + 270 * q^54 + 85 * q^55 - 306 * q^57 + 258 * q^58 + 332 * q^59 - 60 * q^60 - 220 * q^61 + 232 * q^62 + 64 * q^64 - 405 * q^65 + 102 * q^66 + 384 * q^67 + 364 * q^68 - 270 * q^69 - 664 * q^71 + 144 * q^72 - 230 * q^73 - 628 * q^74 + 75 * q^75 - 408 * q^76 - 486 * q^78 + 361 * q^79 - 80 * q^80 + 81 * q^81 - 248 * q^82 - 1172 * q^83 - 455 * q^85 + 868 * q^86 - 387 * q^87 + 136 * q^88 - 40 * q^89 - 180 * q^90 - 360 * q^92 - 348 * q^93 + 994 * q^94 + 510 * q^95 - 96 * q^96 + 175 * q^97 + 306 * 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

3.00000

4.00000

−5.00000

−6.00000

0

−8.00000

−18.0000

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.f		1
5.b	even	2	1		2450.4.a.ba		1
7.b	odd	2	1		70.4.a.b	✓	1
7.c	even	3	2		490.4.e.l		2
7.d	odd	6	2		490.4.e.p		2
21.c	even	2	1		630.4.a.m		1
28.d	even	2	1		560.4.a.k		1
35.c	odd	2	1		350.4.a.t		1
35.f	even	4	2		350.4.c.j		2
56.e	even	2	1		2240.4.a.p		1
56.h	odd	2	1		2240.4.a.w		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.a.b	✓	1	7.b	odd	2	1
350.4.a.t		1	35.c	odd	2	1
350.4.c.j		2	35.f	even	4	2
490.4.a.f		1	1.a	even	1	1	trivial
490.4.e.l		2	7.c	even	3	2
490.4.e.p		2	7.d	odd	6	2
560.4.a.k		1	28.d	even	2	1
630.4.a.m		1	21.c	even	2	1
2240.4.a.p		1	56.e	even	2	1
2240.4.a.w		1	56.h	odd	2	1
2450.4.a.ba		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 $S_{4}^{\mathrm{new}}(\Gamma_0(490))$:

$T_{3} - 3$

$T_{11} + 17$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$
$3$	$T - 3$
$5$	$T + 5$
$7$	$T$
$11$	$T + 17$