LMFDB - Newform orbit 2100.4.a.g

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,4,Mod(1,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, 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("2100.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2100.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:	$123.904011012$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
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 - 3 q^{3} + 7 q^{7} + 9 q^{9}+O(q^{10}) $

$ q - 3 q^{3} + 7 q^{7} + 9 q^{9} + 4 q^{11} - 54 q^{13} + 14 q^{17} + 92 q^{19} - 21 q^{21} + 152 q^{23} - 27 q^{27} - 106 q^{29} - 144 q^{31} - 12 q^{33} - 158 q^{37} + 162 q^{39} - 390 q^{41} + 508 q^{43} + 528 q^{47} + 49 q^{49} - 42 q^{51} - 606 q^{53} - 276 q^{57} - 364 q^{59} + 678 q^{61} + 63 q^{63} - 844 q^{67} - 456 q^{69} - 8 q^{71} + 422 q^{73} + 28 q^{77} + 384 q^{79} + 81 q^{81} + 548 q^{83} + 318 q^{87} + 1194 q^{89} - 378 q^{91} + 432 q^{93} + 1502 q^{97} + 36 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

−3.00000

7.00000

9.00000

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	2100.4.a.g		1
5.b	even	2	1		84.4.a.b	✓	1
5.c	odd	4	2		2100.4.k.g		2
15.d	odd	2	1		252.4.a.a		1
20.d	odd	2	1		336.4.a.e		1
35.c	odd	2	1		588.4.a.a		1
35.i	odd	6	2		588.4.i.h		2
35.j	even	6	2		588.4.i.a		2
40.e	odd	2	1		1344.4.a.p		1
40.f	even	2	1		1344.4.a.b		1
60.h	even	2	1		1008.4.a.d		1
105.g	even	2	1		1764.4.a.l		1
105.o	odd	6	2		1764.4.k.n		2
105.p	even	6	2		1764.4.k.c		2
140.c	even	2	1		2352.4.a.v		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
84.4.a.b	✓	1	5.b	even	2	1
252.4.a.a		1	15.d	odd	2	1
336.4.a.e		1	20.d	odd	2	1
588.4.a.a		1	35.c	odd	2	1
588.4.i.a		2	35.j	even	6	2
588.4.i.h		2	35.i	odd	6	2
1008.4.a.d		1	60.h	even	2	1
1344.4.a.b		1	40.f	even	2	1
1344.4.a.p		1	40.e	odd	2	1
1764.4.a.l		1	105.g	even	2	1
1764.4.k.c		2	105.p	even	6	2
1764.4.k.n		2	105.o	odd	6	2
2100.4.a.g		1	1.a	even	1	1	trivial
2100.4.k.g		2	5.c	odd	4	2
2352.4.a.v		1	140.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2100))$:

$ T_{11} - 4 $

$ T_{13} + 54 $

$ T_{17} - 14 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 3 $ T + 3
$5$	$ T $ T
$7$	$ T - 7 $ T - 7
$11$	$ T - 4 $ T - 4
$13$	$ T + 54 $ T + 54
$17$	$ T - 14 $ T - 14
$19$	$ T - 92 $ T - 92
$23$	$ T - 152 $ T - 152
$29$	$ T + 106 $ T + 106
$31$	$ T + 144 $ T + 144
$37$	$ T + 158 $ T + 158
$41$	$ T + 390 $ T + 390
$43$	$ T - 508 $ T - 508
$47$	$ T - 528 $ T - 528
$53$	$ T + 606 $ T + 606
$59$	$ T + 364 $ T + 364
$61$	$ T - 678 $ T - 678
$67$	$ T + 844 $ T + 844
$71$	$ T + 8 $ T + 8
$73$	$ T - 422 $ T - 422
$79$	$ T - 384 $ T - 384
$83$	$ T - 548 $ T - 548
$89$	$ T - 1194 $ T - 1194
$97$	$ T - 1502 $ T - 1502
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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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2100.a (trivial)

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