LMFDB - Newform orbit 490.4.a.c

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)

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")

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);

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,-1,4,-5,2,0,-8,-26,10,-2] 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} - q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} - 8 q^{8} - 26 q^{9} + 10 q^{10} - 2 q^{11} - 4 q^{12} - 8 q^{13} + 5 q^{15} + 16 q^{16} - 52 q^{17} + 52 q^{18} + 26 q^{19} - 20 q^{20} + 4 q^{22} + 67 q^{23}+ \cdots + 52 q^{99}+O(q^{100})

q - 2 * q^2 - q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 - 8 * q^8 - 26 * q^9 + 10 * q^10 - 2 * q^11 - 4 * q^12 - 8 * q^13 + 5 * q^15 + 16 * q^16 - 52 * q^17 + 52 * q^18 + 26 * q^19 - 20 * q^20 + 4 * q^22 + 67 * q^23 + 8 * q^24 + 25 * q^25 + 16 * q^26 + 53 * q^27 + 69 * q^29 - 10 * q^30 - 332 * q^31 - 32 * q^32 + 2 * q^33 + 104 * q^34 - 104 * q^36 + 196 * q^37 - 52 * q^38 + 8 * q^39 + 40 * q^40 + 353 * q^41 - 369 * q^43 - 8 * q^44 + 130 * q^45 - 134 * q^46 + 88 * q^47 - 16 * q^48 - 50 * q^50 + 52 * q^51 - 32 * q^52 + 582 * q^53 - 106 * q^54 + 10 * q^55 - 26 * q^57 - 138 * q^58 - 350 * q^59 + 20 * q^60 - 467 * q^61 + 664 * q^62 + 64 * q^64 + 40 * q^65 - 4 * q^66 + 291 * q^67 - 208 * q^68 - 67 * q^69 + 770 * q^71 + 208 * q^72 + 628 * q^73 - 392 * q^74 - 25 * q^75 + 104 * q^76 - 16 * q^78 + 1170 * q^79 - 80 * q^80 + 649 * q^81 - 706 * q^82 + 525 * q^83 + 260 * q^85 + 738 * q^86 - 69 * q^87 + 16 * q^88 + 89 * q^89 - 260 * q^90 + 268 * q^92 + 332 * q^93 - 176 * q^94 - 130 * q^95 + 32 * q^96 - 290 * q^97 + 52 * 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

−1.00000

4.00000

−5.00000

2.00000

−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.c		1
5.b	even	2	1		2450.4.a.bg		1
7.b	odd	2	1		490.4.a.e		1
7.c	even	3	2		70.4.e.c	✓	2
7.d	odd	6	2		490.4.e.m		2
21.h	odd	6	2		630.4.k.b		2
28.g	odd	6	2		560.4.q.d		2
35.c	odd	2	1		2450.4.a.be		1
35.j	even	6	2		350.4.e.a		2
35.l	odd	12	4		350.4.j.e		4

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.e.c	✓	2	7.c	even	3	2
350.4.e.a		2	35.j	even	6	2
350.4.j.e		4	35.l	odd	12	4
490.4.a.c		1	1.a	even	1	1	trivial
490.4.a.e		1	7.b	odd	2	1
490.4.e.m		2	7.d	odd	6	2
560.4.q.d		2	28.g	odd	6	2
630.4.k.b		2	21.h	odd	6	2
2450.4.a.be		1	35.c	odd	2	1
2450.4.a.bg		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

T3 + 1

T_{11} + 2

T11 + 2

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$ T + 2
$3$	$T + 1$ T + 1
$5$	$T + 5$ T + 5
$7$	$T$ T
$11$	$T + 2$ T + 2
$13$	$T + 8$ T + 8
$17$	$T + 52$ T + 52
$19$	$T - 26$ T - 26
$23$	$T - 67$ T - 67
$29$	$T - 69$ T - 69
$31$	$T + 332$ T + 332
$37$	$T - 196$ T - 196
$41$	$T - 353$ T - 353
$43$	$T + 369$ T + 369
$47$	$T - 88$ T - 88
$53$	$T - 582$ T - 582
$59$	$T + 350$ T + 350
$61$	$T + 467$ T + 467
$67$	$T - 291$ T - 291
$71$	$T - 770$ T - 770
$73$	$T - 628$ T - 628
$79$	$T - 1170$ T - 1170
$83$	$T - 525$ T - 525
$89$	$T - 89$ T - 89
$97$	$T + 290$ T + 290
show more
show less

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

$n$ :		e.g. 2-40 or 990-1000
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more