Newform orbit 490.4.a.l

• Label: 490.4.a.l
• Level: $490$
• Weight: $4$
• Character orbit: 490.a
• Self dual: yes
• Analytic conductor: $28.911$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$490 = 2 \cdot 5 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	490.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.9109359028$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 2 * q^2 - q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 + 8 * q^8 - 26 * q^9 + 10 * q^10 - 9 * q^11 - 4 * q^12 - 51 * q^13 - 5 * q^15 + 16 * q^16 - 81 * q^17 - 52 * q^18 - 86 * q^19 + 20 * q^20 - 18 * q^22 + 48 * q^23 - 8 * q^24 + 25 * q^25 - 102 * q^26 + 53 * q^27 + 211 * q^29 - 10 * q^30 - 254 * q^31 + 32 * q^32 + 9 * q^33 - 162 * q^34 - 104 * q^36 - 20 * q^37 - 172 * q^38 + 51 * q^39 + 40 * q^40 - 74 * q^41 - 318 * q^43 - 36 * q^44 - 130 * q^45 + 96 * q^46 + 167 * q^47 - 16 * q^48 + 50 * q^50 + 81 * q^51 - 204 * q^52 - 170 * q^53 + 106 * q^54 - 45 * q^55 + 86 * q^57 + 422 * q^58 - 854 * q^59 - 20 * q^60 + 580 * q^61 - 508 * q^62 + 64 * q^64 - 255 * q^65 + 18 * q^66 - 58 * q^67 - 324 * q^68 - 48 * q^69 + 152 * q^71 - 208 * q^72 - 702 * q^73 - 40 * q^74 - 25 * q^75 - 344 * q^76 + 102 * q^78 - 419 * q^79 + 80 * q^80 + 649 * q^81 - 148 * q^82 - 124 * q^83 - 405 * q^85 - 636 * q^86 - 211 * q^87 - 72 * q^88 + 768 * q^89 - 260 * q^90 + 192 * q^92 + 254 * q^93 + 334 * q^94 - 430 * q^95 - 32 * q^96 - 1085 * q^97 + 234 * 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

2.00000

−1.00000

4.00000

5.00000

−2.00000

0

8.00000

−26.0000

10.0000

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	490.4.a.l	✓	1
5.b	even	2	1		2450.4.a.n		1
7.b	odd	2	1		490.4.a.n	yes	1
7.c	even	3	2		490.4.e.e		2
7.d	odd	6	2		490.4.e.d		2
35.c	odd	2	1		2450.4.a.k		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
490.4.a.l	✓	1	1.a	even	1	1	trivial
490.4.a.n	yes	1	7.b	odd	2	1
490.4.e.d		2	7.d	odd	6	2
490.4.e.e		2	7.c	even	3	2
2450.4.a.k		1	35.c	odd	2	1
2450.4.a.n		1	5.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(490))$:

$T_{3} + 1$

$T_{11} + 9$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 2$
$3$	$T + 1$
$5$	$T - 5$
$7$	$T$
$11$	$T + 9$