Newform orbit 490.6.a.i

• Label: 490.6.a.i
• 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 + 23 * q^3 + 16 * q^4 - 25 * q^5 - 92 * q^6 - 64 * q^8 + 286 * q^9 + 100 * q^10 + 555 * q^11 + 368 * q^12 + 241 * q^13 - 575 * q^15 + 256 * q^16 + 1491 * q^17 - 1144 * q^18 + 2038 * q^19 - 400 * q^20 - 2220 * q^22 - 1230 * q^23 - 1472 * q^24 + 625 * q^25 - 964 * q^26 + 989 * q^27 - 5001 * q^29 + 2300 * q^30 - 5696 * q^31 - 1024 * q^32 + 12765 * q^33 - 5964 * q^34 + 4576 * q^36 - 5602 * q^37 - 8152 * q^38 + 5543 * q^39 + 1600 * q^40 + 2424 * q^41 + 602 * q^43 + 8880 * q^44 - 7150 * q^45 + 4920 * q^46 + 23163 * q^47 + 5888 * q^48 - 2500 * q^50 + 34293 * q^51 + 3856 * q^52 - 25296 * q^53 - 3956 * q^54 - 13875 * q^55 + 46874 * q^57 + 20004 * q^58 - 5724 * q^59 - 9200 * q^60 + 36112 * q^61 + 22784 * q^62 + 4096 * q^64 - 6025 * q^65 - 51060 * q^66 + 66104 * q^67 + 23856 * q^68 - 28290 * q^69 + 16080 * q^71 - 18304 * q^72 + 80482 * q^73 + 22408 * q^74 + 14375 * q^75 + 32608 * q^76 - 22172 * q^78 - 64147 * q^79 - 6400 * q^80 - 46751 * q^81 - 9696 * q^82 + 106284 * q^83 - 37275 * q^85 - 2408 * q^86 - 115023 * q^87 - 35520 * q^88 + 71676 * q^89 + 28600 * q^90 - 19680 * q^92 - 131008 * q^93 - 92652 * q^94 - 50950 * q^95 - 23552 * q^96 - 151025 * q^97 + 158730 * 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

23.0000

16.0000

−25.0000

−92.0000

0

−64.0000

286.000

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.i		1
7.b	odd	2	1		70.6.a.a	✓	1
21.c	even	2	1		630.6.a.j		1
28.d	even	2	1		560.6.a.i		1
35.c	odd	2	1		350.6.a.n		1
35.f	even	4	2		350.6.c.h		2

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 23$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(490))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 4$
$3$	$T - 23$
$5$	$T + 25$
$7$	$T$
$11$	$T - 555$