LMFDB - Newform orbit 2535.2.a.f

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2535,2,Mod(1,2535)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2535, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2535.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2535 = 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2535.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:	$20.2420769124$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
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 - q^{3} - 2 q^{4} - q^{5} + 3 q^{7} + q^{9}+O(q^{10}) $

$ q - q^{3} - 2 q^{4} - q^{5} + 3 q^{7} + q^{9} - 3 q^{11} + 2 q^{12} + q^{15} + 4 q^{16} - 3 q^{17} + 2 q^{20} - 3 q^{21} + 3 q^{23} + q^{25} - q^{27} - 6 q^{28} - 6 q^{29} + 6 q^{31} + 3 q^{33} - 3 q^{35} - 2 q^{36} - 9 q^{37} - 3 q^{41} + 10 q^{43} + 6 q^{44} - q^{45} - 12 q^{47} - 4 q^{48} + 2 q^{49} + 3 q^{51} - 3 q^{53} + 3 q^{55} + 12 q^{59} - 2 q^{60} + q^{61} + 3 q^{63} - 8 q^{64} + 6 q^{68} - 3 q^{69} + 9 q^{71} + 6 q^{73} - q^{75} - 9 q^{77} + q^{79} - 4 q^{80} + q^{81} + 6 q^{83} + 6 q^{84} + 3 q^{85} + 6 q^{87} + 15 q^{89} - 6 q^{92} - 6 q^{93} + 9 q^{97} - 3 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

−1.00000

−2.00000

−1.00000

3.00000

1.00000

Atkin-Lehner signs

$ p $	Sign
$3$	$ +1 $
$5$	$ +1 $
$13$	$ -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	2535.2.a.f		1
3.b	odd	2	1		7605.2.a.n		1
13.b	even	2	1		2535.2.a.g		1
13.d	odd	4	2		195.2.b.a	✓	2
39.d	odd	2	1		7605.2.a.i		1
39.f	even	4	2		585.2.b.d		2
52.f	even	4	2		3120.2.g.j		2
65.f	even	4	2		975.2.h.c		2
65.g	odd	4	2		975.2.b.e		2
65.k	even	4	2		975.2.h.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
195.2.b.a	✓	2	13.d	odd	4	2
585.2.b.d		2	39.f	even	4	2
975.2.b.e		2	65.g	odd	4	2
975.2.h.b		2	65.k	even	4	2
975.2.h.c		2	65.f	even	4	2
2535.2.a.f		1	1.a	even	1	1	trivial
2535.2.a.g		1	13.b	even	2	1
3120.2.g.j		2	52.f	even	4	2
7605.2.a.i		1	39.d	odd	2	1
7605.2.a.n		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(2535))$:

$ T_{2} $

$ T_{7} - 3 $

$ T_{11} + 3 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 1 $ T + 1
$5$	$ T + 1 $ T + 1
$7$	$ T - 3 $ T - 3
$11$	$ T + 3 $ T + 3
$13$	$ T $ T
$17$	$ T + 3 $ T + 3
$19$	$ T $ T
$23$	$ T - 3 $ T - 3
$29$	$ T + 6 $ T + 6
$31$	$ T - 6 $ T - 6
$37$	$ T + 9 $ T + 9
$41$	$ T + 3 $ T + 3
$43$	$ T - 10 $ T - 10
$47$	$ T + 12 $ T + 12
$53$	$ T + 3 $ T + 3
$59$	$ T - 12 $ T - 12
$61$	$ T - 1 $ T - 1
$67$	$ T $ T
$71$	$ T - 9 $ T - 9
$73$	$ T - 6 $ T - 6
$79$	$ T - 1 $ T - 1
$83$	$ T - 6 $ T - 6
$89$	$ T - 15 $ T - 15
$97$	$ T - 9 $ T - 9
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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:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2535.a (trivial)

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