LMFDB - Newform orbit 882.4.a.e

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(1,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, 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("882.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.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:	$52.0396846251$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
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 - 2 q^{2} + 4 q^{4} + 6 q^{5} - 8 q^{8}+O(q^{10}) $

$ q - 2 q^{2} + 4 q^{4} + 6 q^{5} - 8 q^{8} - 12 q^{10} - 30 q^{11} - 2 q^{13} + 16 q^{16} + 66 q^{17} + 52 q^{19} + 24 q^{20} + 60 q^{22} - 114 q^{23} - 89 q^{25} + 4 q^{26} - 72 q^{29} + 196 q^{31} - 32 q^{32} - 132 q^{34} - 286 q^{37} - 104 q^{38} - 48 q^{40} - 378 q^{41} + 164 q^{43} - 120 q^{44} + 228 q^{46} - 228 q^{47} + 178 q^{50} - 8 q^{52} + 348 q^{53} - 180 q^{55} + 144 q^{58} - 348 q^{59} + 106 q^{61} - 392 q^{62} + 64 q^{64} - 12 q^{65} + 596 q^{67} + 264 q^{68} - 630 q^{71} + 1042 q^{73} + 572 q^{74} + 208 q^{76} - 88 q^{79} + 96 q^{80} + 756 q^{82} - 1440 q^{83} + 396 q^{85} - 328 q^{86} + 240 q^{88} + 1374 q^{89} - 456 q^{92} + 456 q^{94} + 312 q^{95} + 34 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

−2.00000

4.00000

6.00000

−8.00000

−12.0000

Atkin-Lehner signs

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

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	882.4.a.e		1
3.b	odd	2	1		882.4.a.m		1
7.b	odd	2	1		126.4.a.b	✓	1
7.c	even	3	2		882.4.g.q		2
7.d	odd	6	2		882.4.g.t		2
21.c	even	2	1		126.4.a.g	yes	1
21.g	even	6	2		882.4.g.e		2
21.h	odd	6	2		882.4.g.h		2
28.d	even	2	1		1008.4.a.g		1
84.h	odd	2	1		1008.4.a.n		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
126.4.a.b	✓	1	7.b	odd	2	1
126.4.a.g	yes	1	21.c	even	2	1
882.4.a.e		1	1.a	even	1	1	trivial
882.4.a.m		1	3.b	odd	2	1
882.4.g.e		2	21.g	even	6	2
882.4.g.h		2	21.h	odd	6	2
882.4.g.q		2	7.c	even	3	2
882.4.g.t		2	7.d	odd	6	2
1008.4.a.g		1	28.d	even	2	1
1008.4.a.n		1	84.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(882))$:

$ T_{5} - 6 $

$ T_{11} + 30 $

$ T_{13} + 2 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T $ T
$5$	$ T - 6 $ T - 6
$7$	$ T $ T
$11$	$ T + 30 $ T + 30
$13$	$ T + 2 $ T + 2
$17$	$ T - 66 $ T - 66
$19$	$ T - 52 $ T - 52
$23$	$ T + 114 $ T + 114
$29$	$ T + 72 $ T + 72
$31$	$ T - 196 $ T - 196
$37$	$ T + 286 $ T + 286
$41$	$ T + 378 $ T + 378
$43$	$ T - 164 $ T - 164
$47$	$ T + 228 $ T + 228
$53$	$ T - 348 $ T - 348
$59$	$ T + 348 $ T + 348
$61$	$ T - 106 $ T - 106
$67$	$ T - 596 $ T - 596
$71$	$ T + 630 $ T + 630
$73$	$ T - 1042 $ T - 1042
$79$	$ T + 88 $ T + 88
$83$	$ T + 1440 $ T + 1440
$89$	$ T - 1374 $ T - 1374
$97$	$ T - 34 $ T - 34
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Classical	Maass
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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)

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