LMFDB - Newform orbit 490.4.a.j

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,4,Mod(1,490)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("490.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

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

Newform invariants

comment:select newform

sage:traces = [1,2,-5,4,-5,-10,0,8,-2,-10,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.9109359028$
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

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$

$=$

$ q + 2 q^{2} - 5 q^{3} + 4 q^{4} - 5 q^{5} - 10 q^{6} + 8 q^{8} - 2 q^{9} - 10 q^{10} - q^{11} - 20 q^{12} - 7 q^{13} + 25 q^{15} + 16 q^{16} + 51 q^{17} - 4 q^{18} - 30 q^{19} - 20 q^{20} - 2 q^{22} - 50 q^{23}+ \cdots + 2 q^{99}+O(q^{100}) $

q + 2 * q^2 - 5 * q^3 + 4 * q^4 - 5 * q^5 - 10 * q^6 + 8 * q^8 - 2 * q^9 - 10 * q^10 - q^11 - 20 * q^12 - 7 * q^13 + 25 * q^15 + 16 * q^16 + 51 * q^17 - 4 * q^18 - 30 * q^19 - 20 * q^20 - 2 * q^22 - 50 * q^23 - 40 * q^24 + 25 * q^25 - 14 * q^26 + 145 * q^27 + 79 * q^29 + 50 * q^30 + 212 * q^31 + 32 * q^32 + 5 * q^33 + 102 * q^34 - 8 * q^36 - 190 * q^37 - 60 * q^38 + 35 * q^39 - 40 * q^40 + 308 * q^41 + 422 * q^43 - 4 * q^44 + 10 * q^45 - 100 * q^46 - 121 * q^47 - 80 * q^48 + 50 * q^50 - 255 * q^51 - 28 * q^52 + 664 * q^53 + 290 * q^54 + 5 * q^55 + 150 * q^57 + 158 * q^58 - 628 * q^59 + 100 * q^60 + 684 * q^61 + 424 * q^62 + 64 * q^64 + 35 * q^65 + 10 * q^66 + 1056 * q^67 + 204 * q^68 + 250 * q^69 + 744 * q^71 - 16 * q^72 - 726 * q^73 - 380 * q^74 - 125 * q^75 - 120 * q^76 + 70 * q^78 - 407 * q^79 - 80 * q^80 - 671 * q^81 + 616 * q^82 - 644 * q^83 - 255 * q^85 + 844 * q^86 - 395 * q^87 - 8 * q^88 + 880 * q^89 + 20 * q^90 - 200 * q^92 - 1060 * q^93 - 242 * q^94 + 150 * q^95 - 160 * q^96 + 1351 * q^97 + 2 * 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.

comment:embeddings in the coefficient field

gp:mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

2.00000

−5.00000

4.00000

−5.00000

−10.0000

8.00000

−2.00000

−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.j		1
5.b	even	2	1		2450.4.a.r		1
7.b	odd	2	1		70.4.a.e	✓	1
7.c	even	3	2		490.4.e.g		2
7.d	odd	6	2		490.4.e.c		2
21.c	even	2	1		630.4.a.b		1
28.d	even	2	1		560.4.a.f		1
35.c	odd	2	1		350.4.a.c		1
35.f	even	4	2		350.4.c.k		2
56.e	even	2	1		2240.4.a.bc		1
56.h	odd	2	1		2240.4.a.h		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.a.e	✓	1	7.b	odd	2	1
350.4.a.c		1	35.c	odd	2	1
350.4.c.k		2	35.f	even	4	2
490.4.a.j		1	1.a	even	1	1	trivial
490.4.e.c		2	7.d	odd	6	2
490.4.e.g		2	7.c	even	3	2
560.4.a.f		1	28.d	even	2	1
630.4.a.b		1	21.c	even	2	1
2240.4.a.h		1	56.h	odd	2	1
2240.4.a.bc		1	56.e	even	2	1
2450.4.a.r		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} + 5 $

T3 + 5

$ T_{11} + 1 $

T11 + 1

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T + 5 $ T + 5
$5$	$ T + 5 $ T + 5
$7$	$ T $ T
$11$	$ T + 1 $ T + 1
$13$	$ T + 7 $ T + 7
$17$	$ T - 51 $ T - 51
$19$	$ T + 30 $ T + 30
$23$	$ T + 50 $ T + 50
$29$	$ T - 79 $ T - 79
$31$	$ T - 212 $ T - 212
$37$	$ T + 190 $ T + 190
$41$	$ T - 308 $ T - 308
$43$	$ T - 422 $ T - 422
$47$	$ T + 121 $ T + 121
$53$	$ T - 664 $ T - 664
$59$	$ T + 628 $ T + 628
$61$	$ T - 684 $ T - 684
$67$	$ T - 1056 $ T - 1056
$71$	$ T - 744 $ T - 744
$73$	$ T + 726 $ T + 726
$79$	$ T + 407 $ T + 407
$83$	$ T + 644 $ T + 644
$89$	$ T - 880 $ T - 880
$97$	$ T - 1351 $ T - 1351
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Classical	Maass
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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$
Belyi maps

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

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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