LMFDB - Newform orbit 2695.1.g.e

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2695,1,Mod(1814,2695)] 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("2695.1814"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2695, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2695.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [1,1,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$1.34498020905$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.2695.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.36315125.1
Stark unit:	Root of $x^{6} - 4346502x^{5} - 4356698177x^{4} - 18900801725364x^{3} - 4356698177x^{2} - 4346502x + 1$

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$.

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$1$	$-1$

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} $

1814.1

1.00000

−1.00000

1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
55.d	odd	2	1	CM by $\Q(\sqrt{-55}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2695.1.g.e		1
5.b	even	2	1		2695.1.g.b		1
7.b	odd	2	1		2695.1.g.d		1
7.c	even	3	2		385.1.q.a	✓	2
7.d	odd	6	2		2695.1.q.a		2
11.b	odd	2	1		2695.1.g.b		1
21.h	odd	6	2		3465.1.cd.b		2
35.c	odd	2	1		2695.1.g.a		1
35.i	odd	6	2		2695.1.q.d		2
35.j	even	6	2		385.1.q.b	yes	2
35.l	odd	12	4		1925.1.w.c		4
55.d	odd	2	1	CM	2695.1.g.e		1
77.b	even	2	1		2695.1.g.a		1
77.h	odd	6	2		385.1.q.b	yes	2
77.i	even	6	2		2695.1.q.d		2
105.o	odd	6	2		3465.1.cd.a		2
231.l	even	6	2		3465.1.cd.a		2
385.h	even	2	1		2695.1.g.d		1
385.o	even	6	2		2695.1.q.a		2
385.q	odd	6	2		385.1.q.a	✓	2
385.bc	even	12	4		1925.1.w.c		4
1155.bo	even	6	2		3465.1.cd.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
385.1.q.a	✓	2	7.c	even	3	2
385.1.q.a	✓	2	385.q	odd	6	2
385.1.q.b	yes	2	35.j	even	6	2
385.1.q.b	yes	2	77.h	odd	6	2
1925.1.w.c		4	35.l	odd	12	4
1925.1.w.c		4	385.bc	even	12	4
2695.1.g.a		1	35.c	odd	2	1
2695.1.g.a		1	77.b	even	2	1
2695.1.g.b		1	5.b	even	2	1
2695.1.g.b		1	11.b	odd	2	1
2695.1.g.d		1	7.b	odd	2	1
2695.1.g.d		1	385.h	even	2	1
2695.1.g.e		1	1.a	even	1	1	trivial
2695.1.g.e		1	55.d	odd	2	1	CM
2695.1.q.a		2	7.d	odd	6	2
2695.1.q.a		2	385.o	even	6	2
2695.1.q.d		2	35.i	odd	6	2
2695.1.q.d		2	77.i	even	6	2
3465.1.cd.a		2	105.o	odd	6	2
3465.1.cd.a		2	231.l	even	6	2
3465.1.cd.b		2	21.h	odd	6	2
3465.1.cd.b		2	1155.bo	even	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(2695, [\chi])$:

$ T_{2} - 1 $

T2 - 1

$ T_{3} $

T3

$ T_{13} - 1 $

T13 - 1

$ T_{31} + 1 $

T31 + 1

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 1 $ T - 1
$3$	$ T $ T
$5$	$ T - 1 $ T - 1
$7$	$ T $ T
$11$	$ T - 1 $ T - 1
$13$	$ T - 1 $ T - 1
$17$	$ T + 2 $ T + 2
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T + 1 $ T + 1
$37$	$ T $ T
$41$	$ T $ T
$43$	$ T - 1 $ T - 1
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T + 1 $ T + 1
$61$	$ T $ T
$67$	$ T $ T
$71$	$ T + 1 $ T + 1
$73$	$ T - 1 $ T - 1
$79$	$ T $ T
$83$	$ T - 1 $ T - 1
$89$	$ T + 1 $ T + 1
$97$	$ T $ T
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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2695.g (of order \(2\), degree \(1\), minimal)

\(n\)	\(981\)	\(1816\)	\(2157\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more