LMFDB - Newform orbit 1260.4.a.i

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,4,Mod(1,1260)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1260.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1260.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$74.3424066072$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
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 + 5 q^{5} - 7 q^{7}+O(q^{10}) $

$ q + 5 q^{5} - 7 q^{7} + 7 q^{11} - 23 q^{13} + 25 q^{17} - 62 q^{19} + 86 q^{23} + 25 q^{25} + 29 q^{29} - 12 q^{31} - 35 q^{35} - 150 q^{37} - 204 q^{41} - 178 q^{43} - 33 q^{47} + 49 q^{49} - 452 q^{53} + 35 q^{55} - 120 q^{59} + 920 q^{61} - 115 q^{65} - 300 q^{67} - 520 q^{71} + 370 q^{73} - 49 q^{77} - 1013 q^{79} + 636 q^{83} + 125 q^{85} - 292 q^{89} + 161 q^{91} - 310 q^{95} - 1381 q^{97}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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

5.00000

−7.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$-1$
$3$	$-1$
$5$	$-1$
$7$	$1$

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	1260.4.a.i		1
3.b	odd	2	1		140.4.a.d	✓	1
12.b	even	2	1		560.4.a.h		1
15.d	odd	2	1		700.4.a.g		1
15.e	even	4	2		700.4.e.i		2
21.c	even	2	1		980.4.a.g		1
21.g	even	6	2		980.4.i.k		2
21.h	odd	6	2		980.4.i.i		2
24.f	even	2	1		2240.4.a.u		1
24.h	odd	2	1		2240.4.a.s		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.4.a.d	✓	1	3.b	odd	2	1
560.4.a.h		1	12.b	even	2	1
700.4.a.g		1	15.d	odd	2	1
700.4.e.i		2	15.e	even	4	2
980.4.a.g		1	21.c	even	2	1
980.4.i.i		2	21.h	odd	6	2
980.4.i.k		2	21.g	even	6	2
1260.4.a.i		1	1.a	even	1	1	trivial
2240.4.a.s		1	24.h	odd	2	1
2240.4.a.u		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1260))$:

$ T_{11} - 7 $

$ T_{17} - 25 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 5 $ T - 5
$7$	$ T + 7 $ T + 7
$11$	$ T - 7 $ T - 7
$13$	$ T + 23 $ T + 23
$17$	$ T - 25 $ T - 25
$19$	$ T + 62 $ T + 62
$23$	$ T - 86 $ T - 86
$29$	$ T - 29 $ T - 29
$31$	$ T + 12 $ T + 12
$37$	$ T + 150 $ T + 150
$41$	$ T + 204 $ T + 204
$43$	$ T + 178 $ T + 178
$47$	$ T + 33 $ T + 33
$53$	$ T + 452 $ T + 452
$59$	$ T + 120 $ T + 120
$61$	$ T - 920 $ T - 920
$67$	$ T + 300 $ T + 300
$71$	$ T + 520 $ T + 520
$73$	$ T - 370 $ T - 370
$79$	$ T + 1013 $ T + 1013
$83$	$ T - 636 $ T - 636
$89$	$ T + 292 $ T + 292
$97$	$ T + 1381 $ T + 1381
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1260.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
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