LMFDB - Newform orbit 88.4.a.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [88,4,Mod(1,88)] 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("88.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(88, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	88.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$5.19216808051$
Analytic rank:	$0$
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

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$ q + 7 q^{3} + 9 q^{5} + 2 q^{7} + 22 q^{9} - 11 q^{11} + 63 q^{15} - 38 q^{17} + 44 q^{19} + 14 q^{21} + 175 q^{23} - 44 q^{25} - 35 q^{27} - 264 q^{29} + 159 q^{31} - 77 q^{33} + 18 q^{35} - 173 q^{37}+ \cdots - 242 q^{99}+O(q^{100}) $

q + 7 * q^3 + 9 * q^5 + 2 * q^7 + 22 * q^9 - 11 * q^11 + 63 * q^15 - 38 * q^17 + 44 * q^19 + 14 * q^21 + 175 * q^23 - 44 * q^25 - 35 * q^27 - 264 * q^29 + 159 * q^31 - 77 * q^33 + 18 * q^35 - 173 * q^37 - 220 * q^41 - 542 * q^43 + 198 * q^45 - 264 * q^47 - 339 * q^49 - 266 * q^51 + 682 * q^53 - 99 * q^55 + 308 * q^57 + 421 * q^59 + 308 * q^61 + 44 * q^63 + 177 * q^67 + 1225 * q^69 + 365 * q^71 - 528 * q^73 - 308 * q^75 - 22 * q^77 + 686 * q^79 - 839 * q^81 + 698 * q^83 - 342 * q^85 - 1848 * q^87 + 967 * q^89 + 1113 * q^93 + 396 * q^95 - 1127 * q^97 - 242 * 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

7.00000

9.00000

2.00000

22.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$11$	$ +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	88.4.a.b	✓	1
3.b	odd	2	1		792.4.a.b		1
4.b	odd	2	1		176.4.a.a		1
5.b	even	2	1		2200.4.a.a		1
8.b	even	2	1		704.4.a.a		1
8.d	odd	2	1		704.4.a.k		1
11.b	odd	2	1		968.4.a.e		1
12.b	even	2	1		1584.4.a.g		1
44.c	even	2	1		1936.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
88.4.a.b	✓	1	1.a	even	1	1	trivial
176.4.a.a		1	4.b	odd	2	1
704.4.a.a		1	8.b	even	2	1
704.4.a.k		1	8.d	odd	2	1
792.4.a.b		1	3.b	odd	2	1
968.4.a.e		1	11.b	odd	2	1
1584.4.a.g		1	12.b	even	2	1
1936.4.a.b		1	44.c	even	2	1
2200.4.a.a		1	5.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} - 7 $ T3 - 7 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(88))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 7 $ T - 7
$5$	$ T - 9 $ T - 9
$7$	$ T - 2 $ T - 2
$11$	$ T + 11 $ T + 11
$13$	$ T $ T
$17$	$ T + 38 $ T + 38
$19$	$ T - 44 $ T - 44
$23$	$ T - 175 $ T - 175
$29$	$ T + 264 $ T + 264
$31$	$ T - 159 $ T - 159
$37$	$ T + 173 $ T + 173
$41$	$ T + 220 $ T + 220
$43$	$ T + 542 $ T + 542
$47$	$ T + 264 $ T + 264
$53$	$ T - 682 $ T - 682
$59$	$ T - 421 $ T - 421
$61$	$ T - 308 $ T - 308
$67$	$ T - 177 $ T - 177
$71$	$ T - 365 $ T - 365
$73$	$ T + 528 $ T + 528
$79$	$ T - 686 $ T - 686
$83$	$ T - 698 $ T - 698
$89$	$ T - 967 $ T - 967
$97$	$ T + 1127 $ T + 1127
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

Level:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	88.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