Newform orbit 490.6.a.f

• Label: 490.6.a.f
• 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 + 5 * q^3 + 16 * q^4 + 25 * q^5 - 20 * q^6 - 64 * q^8 - 218 * q^9 - 100 * q^10 + 198 * q^11 + 80 * q^12 + 340 * q^13 + 125 * q^15 + 256 * q^16 - 1848 * q^17 + 872 * q^18 + 1210 * q^19 + 400 * q^20 - 792 * q^22 + 2823 * q^23 - 320 * q^24 + 625 * q^25 - 1360 * q^26 - 2305 * q^27 - 4539 * q^29 - 500 * q^30 + 712 * q^31 - 1024 * q^32 + 990 * q^33 + 7392 * q^34 - 3488 * q^36 - 7324 * q^37 - 4840 * q^38 + 1700 * q^39 - 1600 * q^40 - 15633 * q^41 + 15827 * q^43 + 3168 * q^44 - 5450 * q^45 - 11292 * q^46 + 3192 * q^47 + 1280 * q^48 - 2500 * q^50 - 9240 * q^51 + 5440 * q^52 - 20046 * q^53 + 9220 * q^54 + 4950 * q^55 + 6050 * q^57 + 18156 * q^58 - 23046 * q^59 + 2000 * q^60 + 379 * q^61 - 2848 * q^62 + 4096 * q^64 + 8500 * q^65 - 3960 * q^66 - 35473 * q^67 - 29568 * q^68 + 14115 * q^69 + 71814 * q^71 + 13952 * q^72 - 31664 * q^73 + 29296 * q^74 + 3125 * q^75 + 19360 * q^76 - 6800 * q^78 + 8534 * q^79 + 6400 * q^80 + 41449 * q^81 + 62532 * q^82 + 106551 * q^83 - 46200 * q^85 - 63308 * q^86 - 22695 * q^87 - 12672 * q^88 + 12303 * q^89 + 21800 * q^90 + 45168 * q^92 + 3560 * q^93 - 12768 * q^94 + 30250 * q^95 - 5120 * q^96 + 102802 * q^97 - 43164 * 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

5.00000

16.0000

25.0000

−20.0000

0

−64.0000

−218.000

−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.f		1
7.b	odd	2	1		490.6.a.d		1
7.d	odd	6	2		70.6.e.a	✓	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.6.e.a	✓	2	7.d	odd	6	2
490.6.a.d		1	7.b	odd	2	1
490.6.a.f		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 5$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(490))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 4$
$3$	$T - 5$
$5$	$T - 25$
$7$	$T$
$11$	$T - 198$