Newform orbit 490.6.a.m

• Label: 490.6.a.m
• 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 + 17 * q^3 + 16 * q^4 - 25 * q^5 + 68 * q^6 + 64 * q^8 + 46 * q^9 - 100 * q^10 - 715 * q^11 + 272 * q^12 - 331 * q^13 - 425 * q^15 + 256 * q^16 + 1699 * q^17 + 184 * q^18 + 1718 * q^19 - 400 * q^20 - 2860 * q^22 - 3950 * q^23 + 1088 * q^24 + 625 * q^25 - 1324 * q^26 - 3349 * q^27 + 4579 * q^29 - 1700 * q^30 - 6756 * q^31 + 1024 * q^32 - 12155 * q^33 + 6796 * q^34 + 736 * q^36 - 16518 * q^37 + 6872 * q^38 - 5627 * q^39 - 1600 * q^40 - 18876 * q^41 + 2258 * q^43 - 11440 * q^44 - 1150 * q^45 - 15800 * q^46 + 537 * q^47 + 4352 * q^48 + 2500 * q^50 + 28883 * q^51 - 5296 * q^52 - 10984 * q^53 - 13396 * q^54 + 17875 * q^55 + 29206 * q^57 + 18316 * q^58 + 25956 * q^59 - 6800 * q^60 - 39188 * q^61 - 27024 * q^62 + 4096 * q^64 + 8275 * q^65 - 48620 * q^66 + 4416 * q^67 + 27184 * q^68 - 67150 * q^69 - 31880 * q^71 + 2944 * q^72 + 5018 * q^73 - 66072 * q^74 + 10625 * q^75 + 27488 * q^76 - 22508 * q^78 - 27977 * q^79 - 6400 * q^80 - 68111 * q^81 - 75504 * q^82 - 37644 * q^83 - 42475 * q^85 + 9032 * q^86 + 77843 * q^87 - 45760 * q^88 + 17216 * q^89 - 4600 * q^90 - 63200 * q^92 - 114852 * q^93 + 2148 * q^94 - 42950 * q^95 + 17408 * q^96 + 63175 * q^97 - 32890 * 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

17.0000

16.0000

−25.0000

68.0000

0

64.0000

46.0000

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

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 17$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(490))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 4$
$3$	$T - 17$
$5$	$T + 25$
$7$	$T$
$11$	$T + 715$