LMFDB - Newform orbit 1225.4.a.l

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1225,4,Mod(1,1225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1225, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1225.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1225 = 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1225.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:	$72.2773397570$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-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^{2} + 17 q^{4} + 45 q^{8} - 27 q^{9}+O(q^{10}) $

$ q + 5 q^{2} + 17 q^{4} + 45 q^{8} - 27 q^{9} - 68 q^{11} + 89 q^{16} - 135 q^{18} - 340 q^{22} + 40 q^{23} - 166 q^{29} + 85 q^{32} - 459 q^{36} - 450 q^{37} + 180 q^{43} - 1156 q^{44} + 200 q^{46} - 590 q^{53} - 830 q^{58} - 287 q^{64} + 740 q^{67} + 688 q^{71} - 1215 q^{72} - 2250 q^{74} - 1384 q^{79} + 729 q^{81} + 900 q^{86} - 3060 q^{88} + 680 q^{92} + 1836 q^{99}+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

17.0000

45.0000

−27.0000

Atkin-Lehner signs

$ p $	Sign
$5$	$1$
$7$	$-1$

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by $\Q(\sqrt{-7}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1225.4.a.l		1
5.b	even	2	1		49.4.a.a	✓	1
7.b	odd	2	1	CM	1225.4.a.l		1
15.d	odd	2	1		441.4.a.m		1
20.d	odd	2	1		784.4.a.k		1
35.c	odd	2	1		49.4.a.a	✓	1
35.i	odd	6	2		49.4.c.d		2
35.j	even	6	2		49.4.c.d		2
105.g	even	2	1		441.4.a.m		1
105.o	odd	6	2		441.4.e.a		2
105.p	even	6	2		441.4.e.a		2
140.c	even	2	1		784.4.a.k		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
49.4.a.a	✓	1	5.b	even	2	1
49.4.a.a	✓	1	35.c	odd	2	1
49.4.c.d		2	35.i	odd	6	2
49.4.c.d		2	35.j	even	6	2
441.4.a.m		1	15.d	odd	2	1
441.4.a.m		1	105.g	even	2	1
441.4.e.a		2	105.o	odd	6	2
441.4.e.a		2	105.p	even	6	2
784.4.a.k		1	20.d	odd	2	1
784.4.a.k		1	140.c	even	2	1
1225.4.a.l		1	1.a	even	1	1	trivial
1225.4.a.l		1	7.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1225))$:

$ T_{2} - 5 $

$ T_{3} $

$ T_{19} $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 5 $ T - 5
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T + 68 $ T + 68
$13$	$ T $ T
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T - 40 $ T - 40
$29$	$ T + 166 $ T + 166
$31$	$ T $ T
$37$	$ T + 450 $ T + 450
$41$	$ T $ T
$43$	$ T - 180 $ T - 180
$47$	$ T $ T
$53$	$ T + 590 $ T + 590
$59$	$ T $ T
$61$	$ T $ T
$67$	$ T - 740 $ T - 740
$71$	$ T - 688 $ T - 688
$73$	$ T $ T
$79$	$ T + 1384 $ T + 1384
$83$	$ T $ T
$89$	$ T $ T
$97$	$ 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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1225.a (trivial)

\(n\):		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