LMFDB - Newform orbit 23.4.a.a

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,4,Mod(1,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("23.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$23$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	23.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$1.35704393013$
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

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} - 6 q^{5} + 10 q^{6} - 8 q^{7} + 24 q^{8} - 2 q^{9} + 12 q^{10} + 34 q^{11} + 20 q^{12} - 57 q^{13} + 16 q^{14} + 30 q^{15} - 16 q^{16} - 80 q^{17} + 4 q^{18} - 70 q^{19}+ \cdots - 68 q^{99}+O(q^{100})

q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 6 * q^5 + 10 * q^6 - 8 * q^7 + 24 * q^8 - 2 * q^9 + 12 * q^10 + 34 * q^11 + 20 * q^12 - 57 * q^13 + 16 * q^14 + 30 * q^15 - 16 * q^16 - 80 * q^17 + 4 * q^18 - 70 * q^19 + 24 * q^20 + 40 * q^21 - 68 * q^22 + 23 * q^23 - 120 * q^24 - 89 * q^25 + 114 * q^26 + 145 * q^27 + 32 * q^28 + 245 * q^29 - 60 * q^30 + 103 * q^31 - 160 * q^32 - 170 * q^33 + 160 * q^34 + 48 * q^35 + 8 * q^36 - 298 * q^37 + 140 * q^38 + 285 * q^39 - 144 * q^40 + 95 * q^41 - 80 * q^42 + 88 * q^43 - 136 * q^44 + 12 * q^45 - 46 * q^46 - 357 * q^47 + 80 * q^48 - 279 * q^49 + 178 * q^50 + 400 * q^51 + 228 * q^52 - 414 * q^53 - 290 * q^54 - 204 * q^55 - 192 * q^56 + 350 * q^57 - 490 * q^58 - 408 * q^59 - 120 * q^60 + 822 * q^61 - 206 * q^62 + 16 * q^63 + 448 * q^64 + 342 * q^65 + 340 * q^66 + 926 * q^67 + 320 * q^68 - 115 * q^69 - 96 * q^70 + 335 * q^71 - 48 * q^72 - 899 * q^73 + 596 * q^74 + 445 * q^75 + 280 * q^76 - 272 * q^77 - 570 * q^78 - 1322 * q^79 + 96 * q^80 - 671 * q^81 - 190 * q^82 - 36 * q^83 - 160 * q^84 + 480 * q^85 - 176 * q^86 - 1225 * q^87 + 816 * q^88 - 460 * q^89 - 24 * q^90 + 456 * q^91 - 92 * q^92 - 515 * q^93 + 714 * q^94 + 420 * q^95 + 800 * q^96 - 964 * q^97 + 558 * q^98 - 68 * 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

−6.00000

10.0000

−8.00000

24.0000

−2.00000

12.0000

Atkin-Lehner signs

$p$	Sign
$23$	$-1$

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	23.4.a.a	✓	1
3.b	odd	2	1		207.4.a.a		1
4.b	odd	2	1		368.4.a.d		1
5.b	even	2	1		575.4.a.g		1
5.c	odd	4	2		575.4.b.b		2
7.b	odd	2	1		1127.4.a.a		1
8.b	even	2	1		1472.4.a.h		1
8.d	odd	2	1		1472.4.a.c		1
23.b	odd	2	1		529.4.a.a		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.4.a.a	✓	1	1.a	even	1	1	trivial
207.4.a.a		1	3.b	odd	2	1
368.4.a.d		1	4.b	odd	2	1
529.4.a.a		1	23.b	odd	2	1
575.4.a.g		1	5.b	even	2	1
575.4.b.b		2	5.c	odd	4	2
1127.4.a.a		1	7.b	odd	2	1
1472.4.a.c		1	8.d	odd	2	1
1472.4.a.h		1	8.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 2$ T2 + 2 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(23))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$ T + 2
$3$	$T + 5$ T + 5
$5$	$T + 6$ T + 6
$7$	$T + 8$ T + 8
$11$	$T - 34$ T - 34
$13$	$T + 57$ T + 57
$17$	$T + 80$ T + 80
$19$	$T + 70$ T + 70
$23$	$T - 23$ T - 23
$29$	$T - 245$ T - 245
$31$	$T - 103$ T - 103
$37$	$T + 298$ T + 298
$41$	$T - 95$ T - 95
$43$	$T - 88$ T - 88
$47$	$T + 357$ T + 357
$53$	$T + 414$ T + 414
$59$	$T + 408$ T + 408
$61$	$T - 822$ T - 822
$67$	$T - 926$ T - 926
$71$	$T - 335$ T - 335
$73$	$T + 899$ T + 899
$79$	$T + 1322$ T + 1322
$83$	$T + 36$ T + 36
$89$	$T + 460$ T + 460
$97$	$T + 964$ T + 964
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