LMFDB - Newform orbit 882.4.a.d

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,4,Mod(1,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [1,-2,0,4,2,0,0,-8,0,-4,8,0,42] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
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} + 2 q^{5} - 8 q^{8} - 4 q^{10} + 8 q^{11} + 42 q^{13} + 16 q^{16} - 2 q^{17} + 124 q^{19} + 8 q^{20} - 16 q^{22} - 76 q^{23} - 121 q^{25} - 84 q^{26} - 254 q^{29} + 72 q^{31} - 32 q^{32}+ \cdots + 1190 q^{97}+O(q^{100})

q - 2 * q^2 + 4 * q^4 + 2 * q^5 - 8 * q^8 - 4 * q^10 + 8 * q^11 + 42 * q^13 + 16 * q^16 - 2 * q^17 + 124 * q^19 + 8 * q^20 - 16 * q^22 - 76 * q^23 - 121 * q^25 - 84 * q^26 - 254 * q^29 + 72 * q^31 - 32 * q^32 + 4 * q^34 + 398 * q^37 - 248 * q^38 - 16 * q^40 + 462 * q^41 + 212 * q^43 + 32 * q^44 + 152 * q^46 - 264 * q^47 + 242 * q^50 + 168 * q^52 + 162 * q^53 + 16 * q^55 + 508 * q^58 - 772 * q^59 - 30 * q^61 - 144 * q^62 + 64 * q^64 + 84 * q^65 - 764 * q^67 - 8 * q^68 + 236 * q^71 - 418 * q^73 - 796 * q^74 + 496 * q^76 + 552 * q^79 + 32 * q^80 - 924 * q^82 + 1036 * q^83 - 4 * q^85 - 424 * q^86 - 64 * q^88 + 30 * q^89 - 304 * q^92 + 528 * q^94 + 248 * q^95 + 1190 * q^97

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

2.00000

−8.00000

−4.00000

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.d		1
3.b	odd	2	1		294.4.a.h		1
7.b	odd	2	1		126.4.a.c		1
7.c	even	3	2		882.4.g.r		2
7.d	odd	6	2		882.4.g.s		2
12.b	even	2	1		2352.4.a.ba		1
21.c	even	2	1		42.4.a.b	✓	1
21.g	even	6	2		294.4.e.a		2
21.h	odd	6	2		294.4.e.d		2
28.d	even	2	1		1008.4.a.j		1
84.h	odd	2	1		336.4.a.d		1
105.g	even	2	1		1050.4.a.d		1
105.k	odd	4	2		1050.4.g.n		2
168.e	odd	2	1		1344.4.a.t		1
168.i	even	2	1		1344.4.a.f		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
42.4.a.b	✓	1	21.c	even	2	1
126.4.a.c		1	7.b	odd	2	1
294.4.a.h		1	3.b	odd	2	1
294.4.e.a		2	21.g	even	6	2
294.4.e.d		2	21.h	odd	6	2
336.4.a.d		1	84.h	odd	2	1
882.4.a.d		1	1.a	even	1	1	trivial
882.4.g.r		2	7.c	even	3	2
882.4.g.s		2	7.d	odd	6	2
1008.4.a.j		1	28.d	even	2	1
1050.4.a.d		1	105.g	even	2	1
1050.4.g.n		2	105.k	odd	4	2
1344.4.a.f		1	168.i	even	2	1
1344.4.a.t		1	168.e	odd	2	1
2352.4.a.ba		1	12.b	even	2	1

Hecke kernels

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

T_{5} - 2

T5 - 2

T_{11} - 8

T11 - 8

T_{13} - 42

T13 - 42

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$ T + 2
$3$	$T$ T
$5$	$T - 2$ T - 2
$7$	$T$ T
$11$	$T - 8$ T - 8
$13$	$T - 42$ T - 42
$17$	$T + 2$ T + 2
$19$	$T - 124$ T - 124
$23$	$T + 76$ T + 76
$29$	$T + 254$ T + 254
$31$	$T - 72$ T - 72
$37$	$T - 398$ T - 398
$41$	$T - 462$ T - 462
$43$	$T - 212$ T - 212
$47$	$T + 264$ T + 264
$53$	$T - 162$ T - 162
$59$	$T + 772$ T + 772
$61$	$T + 30$ T + 30
$67$	$T + 764$ T + 764
$71$	$T - 236$ T - 236
$73$	$T + 418$ T + 418
$79$	$T - 552$ T - 552
$83$	$T - 1036$ T - 1036
$89$	$T - 30$ T - 30
$97$	$T - 1190$ T - 1190
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