Newform orbit 490.6.a.b

• Label: 490.6.a.b
• 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 - 18 * q^3 + 16 * q^4 + 25 * q^5 + 72 * q^6 - 64 * q^8 + 81 * q^9 - 100 * q^10 - 505 * q^11 - 288 * q^12 - 897 * q^13 - 450 * q^15 + 256 * q^16 - 782 * q^17 - 324 * q^18 + 1683 * q^19 + 400 * q^20 + 2020 * q^22 - 1371 * q^23 + 1152 * q^24 + 625 * q^25 + 3588 * q^26 + 2916 * q^27 + 4374 * q^29 + 1800 * q^30 - 7600 * q^31 - 1024 * q^32 + 9090 * q^33 + 3128 * q^34 + 1296 * q^36 - 11263 * q^37 - 6732 * q^38 + 16146 * q^39 - 1600 * q^40 - 13493 * q^41 - 6830 * q^43 - 8080 * q^44 + 2025 * q^45 + 5484 * q^46 - 19067 * q^47 - 4608 * q^48 - 2500 * q^50 + 14076 * q^51 - 14352 * q^52 + 12569 * q^53 - 11664 * q^54 - 12625 * q^55 - 30294 * q^57 - 17496 * q^58 - 26488 * q^59 - 7200 * q^60 - 18224 * q^61 + 30400 * q^62 + 4096 * q^64 - 22425 * q^65 - 36360 * q^66 - 13032 * q^67 - 12512 * q^68 + 24678 * q^69 + 77056 * q^71 - 5184 * q^72 + 2540 * q^73 + 45052 * q^74 - 11250 * q^75 + 26928 * q^76 - 64584 * q^78 - 530 * q^79 + 6400 * q^80 - 72171 * q^81 + 53972 * q^82 - 78344 * q^83 - 19550 * q^85 + 27320 * q^86 - 78732 * q^87 + 32320 * q^88 + 90758 * q^89 - 8100 * q^90 - 21936 * q^92 + 136800 * q^93 + 76268 * q^94 + 42075 * q^95 + 18432 * q^96 + 116750 * q^97 - 40905 * 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

−18.0000

16.0000

25.0000

72.0000

0

−64.0000

81.0000

−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.b		1
7.b	odd	2	1		490.6.a.h		1
7.c	even	3	2		70.6.e.b	✓	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.6.e.b	✓	2	7.c	even	3	2
490.6.a.b		1	1.a	even	1	1	trivial
490.6.a.h		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} + 18$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(490))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 4$
$3$	$T + 18$
$5$	$T - 25$
$7$	$T$
$11$	$T + 505$