LMFDB - Newform orbit 90.4.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,4,Mod(1,90)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("90.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	90.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$5.31017190052$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
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} + 4 q^{4} - 5 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10}) $

$ q - 2 q^{2} + 4 q^{4} - 5 q^{5} - 4 q^{7} - 8 q^{8} + 10 q^{10} - 12 q^{11} - 58 q^{13} + 8 q^{14} + 16 q^{16} - 66 q^{17} - 100 q^{19} - 20 q^{20} + 24 q^{22} - 132 q^{23} + 25 q^{25} + 116 q^{26} - 16 q^{28} + 90 q^{29} + 152 q^{31} - 32 q^{32} + 132 q^{34} + 20 q^{35} - 34 q^{37} + 200 q^{38} + 40 q^{40} + 438 q^{41} + 32 q^{43} - 48 q^{44} + 264 q^{46} + 204 q^{47} - 327 q^{49} - 50 q^{50} - 232 q^{52} - 222 q^{53} + 60 q^{55} + 32 q^{56} - 180 q^{58} - 420 q^{59} + 902 q^{61} - 304 q^{62} + 64 q^{64} + 290 q^{65} - 1024 q^{67} - 264 q^{68} - 40 q^{70} - 432 q^{71} + 362 q^{73} + 68 q^{74} - 400 q^{76} + 48 q^{77} - 160 q^{79} - 80 q^{80} - 876 q^{82} - 72 q^{83} + 330 q^{85} - 64 q^{86} + 96 q^{88} - 810 q^{89} + 232 q^{91} - 528 q^{92} - 408 q^{94} + 500 q^{95} + 1106 q^{97} + 654 q^{98}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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

4.00000

−5.00000

−4.00000

−8.00000

10.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$1$
$3$	$-1$
$5$	$1$

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	90.4.a.a		1
3.b	odd	2	1		10.4.a.a	✓	1
4.b	odd	2	1		720.4.a.j		1
5.b	even	2	1		450.4.a.q		1
5.c	odd	4	2		450.4.c.d		2
9.c	even	3	2		810.4.e.w		2
9.d	odd	6	2		810.4.e.c		2
12.b	even	2	1		80.4.a.f		1
15.d	odd	2	1		50.4.a.c		1
15.e	even	4	2		50.4.b.a		2
21.c	even	2	1		490.4.a.o		1
21.g	even	6	2		490.4.e.a		2
21.h	odd	6	2		490.4.e.i		2
24.f	even	2	1		320.4.a.b		1
24.h	odd	2	1		320.4.a.m		1
33.d	even	2	1		1210.4.a.b		1
39.d	odd	2	1		1690.4.a.a		1
48.i	odd	4	2		1280.4.d.j		2
48.k	even	4	2		1280.4.d.g		2
60.h	even	2	1		400.4.a.b		1
60.l	odd	4	2		400.4.c.c		2
105.g	even	2	1		2450.4.a.b		1
120.i	odd	2	1		1600.4.a.d		1
120.m	even	2	1		1600.4.a.bx		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
10.4.a.a	✓	1	3.b	odd	2	1
50.4.a.c		1	15.d	odd	2	1
50.4.b.a		2	15.e	even	4	2
80.4.a.f		1	12.b	even	2	1
90.4.a.a		1	1.a	even	1	1	trivial
320.4.a.b		1	24.f	even	2	1
320.4.a.m		1	24.h	odd	2	1
400.4.a.b		1	60.h	even	2	1
400.4.c.c		2	60.l	odd	4	2
450.4.a.q		1	5.b	even	2	1
450.4.c.d		2	5.c	odd	4	2
490.4.a.o		1	21.c	even	2	1
490.4.e.a		2	21.g	even	6	2
490.4.e.i		2	21.h	odd	6	2
720.4.a.j		1	4.b	odd	2	1
810.4.e.c		2	9.d	odd	6	2
810.4.e.w		2	9.c	even	3	2
1210.4.a.b		1	33.d	even	2	1
1280.4.d.g		2	48.k	even	4	2
1280.4.d.j		2	48.i	odd	4	2
1600.4.a.d		1	120.i	odd	2	1
1600.4.a.bx		1	120.m	even	2	1
1690.4.a.a		1	39.d	odd	2	1
2450.4.a.b		1	105.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(90))$:

$ T_{7} + 4 $

$ T_{11} + 12 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T $ T
$5$	$ T + 5 $ T + 5
$7$	$ T + 4 $ T + 4
$11$	$ T + 12 $ T + 12
$13$	$ T + 58 $ T + 58
$17$	$ T + 66 $ T + 66
$19$	$ T + 100 $ T + 100
$23$	$ T + 132 $ T + 132
$29$	$ T - 90 $ T - 90
$31$	$ T - 152 $ T - 152
$37$	$ T + 34 $ T + 34
$41$	$ T - 438 $ T - 438
$43$	$ T - 32 $ T - 32
$47$	$ T - 204 $ T - 204
$53$	$ T + 222 $ T + 222
$59$	$ T + 420 $ T + 420
$61$	$ T - 902 $ T - 902
$67$	$ T + 1024 $ T + 1024
$71$	$ T + 432 $ T + 432
$73$	$ T - 362 $ T - 362
$79$	$ T + 160 $ T + 160
$83$	$ T + 72 $ T + 72
$89$	$ T + 810 $ T + 810
$97$	$ T - 1106 $ T - 1106
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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	90.a (trivial)

\(n\):		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