LMFDB - Newform orbit 1760.1.o.c

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1760,1,Mod(1649,1760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1760.1649"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 1760 = 2^{5} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1760.o (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.440.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.30976000.1
Stark unit:	Root of $x^{6} - 21686x^{5} + 1404835x^{4} - 467516300x^{3} + 1404835x^{2} - 21686x + 1$

$q$-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 $\left(\mathbb{Z}/1760\mathbb{Z}\right)^\times$.

$n$	$321$	$991$	$1057$	$1541$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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} $

1649.1

1.00000

−1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
440.o	odd	2	1	CM by $\Q(\sqrt{-110}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1760.1.o.c		1
4.b	odd	2	1		440.1.o.a	✓	1
5.b	even	2	1		1760.1.o.b		1
8.b	even	2	1		1760.1.o.a		1
8.d	odd	2	1		440.1.o.b	yes	1
11.b	odd	2	1		1760.1.o.d		1
12.b	even	2	1		3960.1.x.c		1
20.d	odd	2	1		440.1.o.d	yes	1
20.e	even	4	2		2200.1.d.f		2
24.f	even	2	1		3960.1.x.d		1
40.e	odd	2	1		440.1.o.c	yes	1
40.f	even	2	1		1760.1.o.d		1
40.k	even	4	2		2200.1.d.e		2
44.c	even	2	1		440.1.o.c	yes	1
55.d	odd	2	1		1760.1.o.a		1
60.h	even	2	1		3960.1.x.b		1
88.b	odd	2	1		1760.1.o.b		1
88.g	even	2	1		440.1.o.d	yes	1
120.m	even	2	1		3960.1.x.a		1
132.d	odd	2	1		3960.1.x.a		1
220.g	even	2	1		440.1.o.b	yes	1
220.i	odd	4	2		2200.1.d.e		2
264.p	odd	2	1		3960.1.x.b		1
440.c	even	2	1		440.1.o.a	✓	1
440.o	odd	2	1	CM	1760.1.o.c		1
440.w	odd	4	2		2200.1.d.f		2
660.g	odd	2	1		3960.1.x.d		1
1320.b	odd	2	1		3960.1.x.c		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
440.1.o.a	✓	1	4.b	odd	2	1
440.1.o.a	✓	1	440.c	even	2	1
440.1.o.b	yes	1	8.d	odd	2	1
440.1.o.b	yes	1	220.g	even	2	1
440.1.o.c	yes	1	40.e	odd	2	1
440.1.o.c	yes	1	44.c	even	2	1
440.1.o.d	yes	1	20.d	odd	2	1
440.1.o.d	yes	1	88.g	even	2	1
1760.1.o.a		1	8.b	even	2	1
1760.1.o.a		1	55.d	odd	2	1
1760.1.o.b		1	5.b	even	2	1
1760.1.o.b		1	88.b	odd	2	1
1760.1.o.c		1	1.a	even	1	1	trivial
1760.1.o.c		1	440.o	odd	2	1	CM
1760.1.o.d		1	11.b	odd	2	1
1760.1.o.d		1	40.f	even	2	1
2200.1.d.e		2	40.k	even	4	2
2200.1.d.e		2	220.i	odd	4	2
2200.1.d.f		2	20.e	even	4	2
2200.1.d.f		2	440.w	odd	4	2
3960.1.x.a		1	120.m	even	2	1
3960.1.x.a		1	132.d	odd	2	1
3960.1.x.b		1	60.h	even	2	1
3960.1.x.b		1	264.p	odd	2	1
3960.1.x.c		1	12.b	even	2	1
3960.1.x.c		1	1320.b	odd	2	1
3960.1.x.d		1	24.f	even	2	1
3960.1.x.d		1	660.g	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(1760, [\chi])$:

$ T_{3} - 1 $

T3 - 1

$ T_{7} + 1 $

T7 + 1

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 1 $ T - 1
$5$	$ T - 1 $ T - 1
$7$	$ T + 1 $ T + 1
$11$	$ T - 1 $ T - 1
$13$	$ T $ T
$17$	$ T - 1 $ T - 1
$19$	$ T + 1 $ T + 1
$23$	$ T $ T
$29$	$ T - 1 $ T - 1
$31$	$ T - 1 $ T - 1
$37$	$ T + 1 $ T + 1
$41$	$ T $ T
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T + 1 $ T + 1
$59$	$ T $ T
$61$	$ T - 1 $ T - 1
$67$	$ T + 2 $ T + 2
$71$	$ T - 1 $ T - 1
$73$	$ T + 2 $ T + 2
$79$	$ T $ T
$83$	$ T $ T
$89$	$ T + 1 $ T + 1
$97$	$ T $ T
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Level:	\( N \)	\(=\)	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1760.o (of order \(2\), degree \(1\), not minimal)

\(n\)	\(321\)	\(991\)	\(1057\)	\(1541\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)	\(-1\)

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