Newform orbit 490.6.a.c

• Label: 490.6.a.c
• 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 - 11 * q^3 + 16 * q^4 + 25 * q^5 + 44 * q^6 - 64 * q^8 - 122 * q^9 - 100 * q^10 + 83 * q^11 - 176 * q^12 + 83 * q^13 - 275 * q^15 + 256 * q^16 + 177 * q^17 + 488 * q^18 + 2082 * q^19 + 400 * q^20 - 332 * q^22 - 3170 * q^23 + 704 * q^24 + 625 * q^25 - 332 * q^26 + 4015 * q^27 - 8681 * q^29 + 1100 * q^30 - 1636 * q^31 - 1024 * q^32 - 913 * q^33 - 708 * q^34 - 1952 * q^36 + 4298 * q^37 - 8328 * q^38 - 913 * q^39 - 1600 * q^40 - 2356 * q^41 + 8738 * q^43 + 1328 * q^44 - 3050 * q^45 + 12680 * q^46 + 3641 * q^47 - 2816 * q^48 - 2500 * q^50 - 1947 * q^51 + 1328 * q^52 + 33268 * q^53 - 16060 * q^54 + 2075 * q^55 - 22902 * q^57 + 34724 * q^58 + 30968 * q^59 - 4400 * q^60 - 4560 * q^61 + 6544 * q^62 + 4096 * q^64 + 2075 * q^65 + 3652 * q^66 + 37788 * q^67 + 2832 * q^68 + 34870 * q^69 - 59304 * q^71 + 7808 * q^72 + 8910 * q^73 - 17192 * q^74 - 6875 * q^75 + 33312 * q^76 + 3652 * q^78 + 27589 * q^79 + 6400 * q^80 - 14519 * q^81 + 9424 * q^82 - 67676 * q^83 + 4425 * q^85 - 34952 * q^86 + 95491 * q^87 - 5312 * q^88 - 10700 * q^89 + 12200 * q^90 - 50720 * q^92 + 17996 * q^93 - 14564 * q^94 + 52050 * q^95 + 11264 * q^96 - 65075 * q^97 - 10126 * 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.c		1
7.b	odd	2	1		70.6.a.d	✓	1
21.c	even	2	1		630.6.a.l		1
28.d	even	2	1		560.6.a.a		1
35.c	odd	2	1		350.6.a.h		1
35.f	even	4	2		350.6.c.c		2

    

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

$p$	$F_p(T)$
$2$	$T + 4$
$3$	$T + 11$
$5$	$T - 25$
$7$	$T$
$11$	$T - 83$