LMFDB - Newform orbit 1360.4.a.i

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1360,4,Mod(1,1360)] 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("1360.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1360, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1360.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,7,0,5,0,22,0,22,0,64] 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:	$80.2425976078$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
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} + 5 q^{5} + 22 q^{7} + 22 q^{9} + 64 q^{11} + 73 q^{13} + 35 q^{15} - 17 q^{17} + 49 q^{19} + 154 q^{21} - 110 q^{23} + 25 q^{25} - 35 q^{27} + 155 q^{29} + 197 q^{31} + 448 q^{33} + 110 q^{35}+ \cdots + 1408 q^{99}+O(q^{100}) $

q + 7 * q^3 + 5 * q^5 + 22 * q^7 + 22 * q^9 + 64 * q^11 + 73 * q^13 + 35 * q^15 - 17 * q^17 + 49 * q^19 + 154 * q^21 - 110 * q^23 + 25 * q^25 - 35 * q^27 + 155 * q^29 + 197 * q^31 + 448 * q^33 + 110 * q^35 - 372 * q^37 + 511 * q^39 - 262 * q^41 - 258 * q^43 + 110 * q^45 + 13 * q^47 + 141 * q^49 - 119 * q^51 - 653 * q^53 + 320 * q^55 + 343 * q^57 + 333 * q^59 - 355 * q^61 + 484 * q^63 + 365 * q^65 - 814 * q^67 - 770 * q^69 - 47 * q^71 - 437 * q^73 + 175 * q^75 + 1408 * q^77 + 384 * q^79 - 839 * q^81 + 736 * q^83 - 85 * q^85 + 1085 * q^87 + 511 * q^89 + 1606 * q^91 + 1379 * q^93 + 245 * q^95 + 537 * q^97 + 1408 * 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

5.00000

22.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$5$	$ -1 $
$17$	$ +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	1360.4.a.i		1
4.b	odd	2	1		85.4.a.a	✓	1
12.b	even	2	1		765.4.a.b		1
20.d	odd	2	1		425.4.a.c		1
20.e	even	4	2		425.4.b.a		2
68.d	odd	2	1		1445.4.a.h		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
85.4.a.a	✓	1	4.b	odd	2	1
425.4.a.c		1	20.d	odd	2	1
425.4.b.a		2	20.e	even	4	2
765.4.a.b		1	12.b	even	2	1
1360.4.a.i		1	1.a	even	1	1	trivial
1445.4.a.h		1	68.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1360))$:

$ T_{3} - 7 $

T3 - 7

$ T_{7} - 22 $

T7 - 22

$ T_{11} - 64 $

T11 - 64

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 7 $ T - 7
$5$	$ T - 5 $ T - 5
$7$	$ T - 22 $ T - 22
$11$	$ T - 64 $ T - 64
$13$	$ T - 73 $ T - 73
$17$	$ T + 17 $ T + 17
$19$	$ T - 49 $ T - 49
$23$	$ T + 110 $ T + 110
$29$	$ T - 155 $ T - 155
$31$	$ T - 197 $ T - 197
$37$	$ T + 372 $ T + 372
$41$	$ T + 262 $ T + 262
$43$	$ T + 258 $ T + 258
$47$	$ T - 13 $ T - 13
$53$	$ T + 653 $ T + 653
$59$	$ T - 333 $ T - 333
$61$	$ T + 355 $ T + 355
$67$	$ T + 814 $ T + 814
$71$	$ T + 47 $ T + 47
$73$	$ T + 437 $ T + 437
$79$	$ T - 384 $ T - 384
$83$	$ T - 736 $ T - 736
$89$	$ T - 511 $ T - 511
$97$	$ T - 537 $ T - 537
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:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1360.a (trivial)

\(n\):		e.g. 2-40 or 80-90
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more