Newform orbit 490.6.a.l

• Label: 490.6.a.l
• Level: $490$
• Weight: $6$
• Character orbit: 490.a
• Self dual: yes
• Analytic conductor: $78.588$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$490 = 2 \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	490.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$78.5880717084$
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 + 4 * q^2 + 11 * q^3 + 16 * q^4 + 25 * q^5 + 44 * q^6 + 64 * q^8 - 122 * q^9 + 100 * q^10 - 267 * q^11 + 176 * q^12 + 1087 * q^13 + 275 * q^15 + 256 * q^16 + 513 * q^17 - 488 * q^18 + 802 * q^19 + 400 * q^20 - 1068 * q^22 - 1290 * q^23 + 704 * q^24 + 625 * q^25 + 4348 * q^26 - 4015 * q^27 + 1779 * q^29 + 1100 * q^30 + 2584 * q^31 + 1024 * q^32 - 2937 * q^33 + 2052 * q^34 - 1952 * q^36 + 13862 * q^37 + 3208 * q^38 + 11957 * q^39 + 1600 * q^40 + 11904 * q^41 - 598 * q^43 - 4272 * q^44 - 3050 * q^45 - 5160 * q^46 + 17019 * q^47 + 2816 * q^48 + 2500 * q^50 + 5643 * q^51 + 17392 * q^52 + 27852 * q^53 - 16060 * q^54 - 6675 * q^55 + 8822 * q^57 + 7116 * q^58 - 30912 * q^59 + 4400 * q^60 + 1780 * q^61 + 10336 * q^62 + 4096 * q^64 + 27175 * q^65 - 11748 * q^66 + 25052 * q^67 + 8208 * q^68 - 14190 * q^69 - 51984 * q^71 - 7808 * q^72 - 47690 * q^73 + 55448 * q^74 + 6875 * q^75 + 12832 * q^76 + 47828 * q^78 - 102121 * q^79 + 6400 * q^80 - 14519 * q^81 + 47616 * q^82 + 83676 * q^83 + 12825 * q^85 - 2392 * q^86 + 19569 * q^87 - 17088 * q^88 + 32400 * q^89 - 12200 * q^90 - 20640 * q^92 + 28424 * q^93 + 68076 * q^94 + 20050 * q^95 + 11264 * q^96 + 148645 * q^97 + 32574 * 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

4.00000

11.0000

16.0000

25.0000

44.0000

0

64.0000

−122.000

100.000

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	490.6.a.l		1
7.b	odd	2	1		70.6.a.f	✓	1
21.c	even	2	1		630.6.a.e		1
28.d	even	2	1		560.6.a.f		1
35.c	odd	2	1		350.6.a.d		1
35.f	even	4	2		350.6.c.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.6.a.f	✓	1	7.b	odd	2	1
350.6.a.d		1	35.c	odd	2	1
350.6.c.b		2	35.f	even	4	2
490.6.a.l		1	1.a	even	1	1	trivial
560.6.a.f		1	28.d	even	2	1
630.6.a.e		1	21.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 11$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(490))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 4$
$3$	$T - 11$
$5$	$T - 25$
$7$	$T$
$11$	$T + 267$