Newform orbit 490.8.a.c

• Label: 490.8.a.c
• Level: $490$
• Weight: $8$
• Character orbit: 490.a
• Self dual: yes
• Analytic conductor: $153.069$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$490 = 2 \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	490.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$153.068662487$
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 + 8 * q^2 - 9 * q^3 + 64 * q^4 + 125 * q^5 - 72 * q^6 + 512 * q^8 - 2106 * q^9 + 1000 * q^10 - 2335 * q^11 - 576 * q^12 + 327 * q^13 - 1125 * q^15 + 4096 * q^16 + 29273 * q^17 - 16848 * q^18 - 6378 * q^19 + 8000 * q^20 - 18680 * q^22 - 10350 * q^23 - 4608 * q^24 + 15625 * q^25 + 2616 * q^26 + 38637 * q^27 - 118509 * q^29 - 9000 * q^30 + 81364 * q^31 + 32768 * q^32 + 21015 * q^33 + 234184 * q^34 - 134784 * q^36 + 14354 * q^37 - 51024 * q^38 - 2943 * q^39 + 64000 * q^40 + 79964 * q^41 - 241706 * q^43 - 149440 * q^44 - 263250 * q^45 - 82800 * q^46 - 338041 * q^47 - 36864 * q^48 + 125000 * q^50 - 263457 * q^51 + 20928 * q^52 - 1344172 * q^53 + 309096 * q^54 - 291875 * q^55 + 57402 * q^57 - 948072 * q^58 - 1722056 * q^59 - 72000 * q^60 - 328528 * q^61 + 650912 * q^62 + 262144 * q^64 + 40875 * q^65 + 168120 * q^66 - 93468 * q^67 + 1873472 * q^68 + 93150 * q^69 - 666920 * q^71 - 1078272 * q^72 - 4750946 * q^73 + 114832 * q^74 - 140625 * q^75 - 408192 * q^76 - 23544 * q^78 + 5507107 * q^79 + 512000 * q^80 + 4258089 * q^81 + 639712 * q^82 - 5460292 * q^83 + 3659125 * q^85 - 1933648 * q^86 + 1066581 * q^87 - 1195520 * q^88 - 6010796 * q^89 - 2106000 * q^90 - 662400 * q^92 - 732276 * q^93 - 2704328 * q^94 - 797250 * q^95 - 294912 * q^96 - 1936235 * q^97 + 4917510 * 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

8.00000

−9.00000

64.0000

125.000

−72.0000

0

512.000

−2106.00

1000.00

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	490.8.a.c		1
7.b	odd	2	1		70.8.a.b	✓	1
28.d	even	2	1		560.8.a.a		1
35.c	odd	2	1		350.8.a.a		1
35.f	even	4	2		350.8.c.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.8.a.b	✓	1	7.b	odd	2	1
350.8.a.a		1	35.c	odd	2	1
350.8.c.c		2	35.f	even	4	2
490.8.a.c		1	1.a	even	1	1	trivial
560.8.a.a		1	28.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} + 9$ acting on $S_{8}^{\mathrm{new}}(\Gamma_0(490))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 8$
$3$	$T + 9$
$5$	$T - 125$
$7$	$T$
$11$	$T + 2335$