LMFDB - Newform orbit 882.4.a.h

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 42)
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} - 15 q^{5} + 8 q^{8}+O(q^{10}) $

$ q + 2 q^{2} + 4 q^{4} - 15 q^{5} + 8 q^{8} - 30 q^{10} + 9 q^{11} + 88 q^{13} + 16 q^{16} - 84 q^{17} - 104 q^{19} - 60 q^{20} + 18 q^{22} + 84 q^{23} + 100 q^{25} + 176 q^{26} - 51 q^{29} - 185 q^{31} + 32 q^{32} - 168 q^{34} + 44 q^{37} - 208 q^{38} - 120 q^{40} - 168 q^{41} + 326 q^{43} + 36 q^{44} + 168 q^{46} - 138 q^{47} + 200 q^{50} + 352 q^{52} - 639 q^{53} - 135 q^{55} - 102 q^{58} + 159 q^{59} - 722 q^{61} - 370 q^{62} + 64 q^{64} - 1320 q^{65} - 166 q^{67} - 336 q^{68} - 1086 q^{71} - 218 q^{73} + 88 q^{74} - 416 q^{76} - 583 q^{79} - 240 q^{80} - 336 q^{82} - 597 q^{83} + 1260 q^{85} + 652 q^{86} + 72 q^{88} - 1038 q^{89} + 336 q^{92} - 276 q^{94} + 1560 q^{95} + 169 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

−15.0000

8.00000

−30.0000

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.h		1
3.b	odd	2	1		294.4.a.g		1
7.b	odd	2	1		882.4.a.r		1
7.c	even	3	2		882.4.g.l		2
7.d	odd	6	2		126.4.g.a		2
12.b	even	2	1		2352.4.a.q		1
21.c	even	2	1		294.4.a.a		1
21.g	even	6	2		42.4.e.b	✓	2
21.h	odd	6	2		294.4.e.e		2
84.h	odd	2	1		2352.4.a.u		1
84.j	odd	6	2		336.4.q.d		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
42.4.e.b	✓	2	21.g	even	6	2
126.4.g.a		2	7.d	odd	6	2
294.4.a.a		1	21.c	even	2	1
294.4.a.g		1	3.b	odd	2	1
294.4.e.e		2	21.h	odd	6	2
336.4.q.d		2	84.j	odd	6	2
882.4.a.h		1	1.a	even	1	1	trivial
882.4.a.r		1	7.b	odd	2	1
882.4.g.l		2	7.c	even	3	2
2352.4.a.q		1	12.b	even	2	1
2352.4.a.u		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} + 15 $

$ T_{11} - 9 $

$ T_{13} - 88 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T $ T
$5$	$ T + 15 $ T + 15
$7$	$ T $ T
$11$	$ T - 9 $ T - 9
$13$	$ T - 88 $ T - 88
$17$	$ T + 84 $ T + 84
$19$	$ T + 104 $ T + 104
$23$	$ T - 84 $ T - 84
$29$	$ T + 51 $ T + 51
$31$	$ T + 185 $ T + 185
$37$	$ T - 44 $ T - 44
$41$	$ T + 168 $ T + 168
$43$	$ T - 326 $ T - 326
$47$	$ T + 138 $ T + 138
$53$	$ T + 639 $ T + 639
$59$	$ T - 159 $ T - 159
$61$	$ T + 722 $ T + 722
$67$	$ T + 166 $ T + 166
$71$	$ T + 1086 $ T + 1086
$73$	$ T + 218 $ T + 218
$79$	$ T + 583 $ T + 583
$83$	$ T + 597 $ T + 597
$89$	$ T + 1038 $ T + 1038
$97$	$ T - 169 $ T - 169
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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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