Newform orbit 490.6.a.e

• Label: 490.6.a.e
• Level: $490$
• Weight: $6$
• Character orbit: 490.a
• Self dual: yes
• Analytic conductor: $78.588$
• Analytic rank: $1$
• 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:	$1$
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 - 4 * q^2 + 3 * q^3 + 16 * q^4 + 25 * q^5 - 12 * q^6 - 64 * q^8 - 234 * q^9 - 100 * q^10 + 405 * q^11 + 48 * q^12 + 391 * q^13 + 75 * q^15 + 256 * q^16 - 999 * q^17 + 936 * q^18 - 2342 * q^19 + 400 * q^20 - 1620 * q^22 + 2430 * q^23 - 192 * q^24 + 625 * q^25 - 1564 * q^26 - 1431 * q^27 + 8259 * q^29 - 300 * q^30 - 4016 * q^31 - 1024 * q^32 + 1215 * q^33 + 3996 * q^34 - 3744 * q^36 - 7042 * q^37 + 9368 * q^38 + 1173 * q^39 - 1600 * q^40 - 3336 * q^41 - 23518 * q^43 + 6480 * q^44 - 5850 * q^45 - 9720 * q^46 - 10317 * q^47 + 768 * q^48 - 2500 * q^50 - 2997 * q^51 + 6256 * q^52 + 3084 * q^53 + 5724 * q^54 + 10125 * q^55 - 7026 * q^57 - 33036 * q^58 + 18816 * q^59 + 1200 * q^60 - 21668 * q^61 + 16064 * q^62 + 4096 * q^64 + 9775 * q^65 - 4860 * q^66 + 52124 * q^67 - 15984 * q^68 + 7290 * q^69 - 28560 * q^71 + 14976 * q^72 + 70342 * q^73 + 28168 * q^74 + 1875 * q^75 - 37472 * q^76 - 4692 * q^78 + 58823 * q^79 + 6400 * q^80 + 52569 * q^81 + 13344 * q^82 - 756 * q^83 - 24975 * q^85 + 94072 * q^86 + 24777 * q^87 - 25920 * q^88 - 135384 * q^89 + 23400 * q^90 + 38880 * q^92 - 12048 * q^93 + 41268 * q^94 - 58550 * q^95 - 3072 * q^96 - 110435 * q^97 - 94770 * 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

3.00000

16.0000

25.0000

−12.0000

0

−64.0000

−234.000

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

    

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

Hecke kernels

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

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 4$
$3$	$T - 3$
$5$	$T - 25$
$7$	$T$
$11$	$T - 405$