LMFDB - Newform orbit 1089.4.a.e

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1089,4,Mod(1,1089)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1089, 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("1089.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$1089 = 3^{2} \cdot 11^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1089.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,0,-7,4,0,26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$64.2530799963$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 33)
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^{2} - 7 q^{4} + 4 q^{5} + 26 q^{7} + 15 q^{8} - 4 q^{10} + 32 q^{13} - 26 q^{14} + 41 q^{16} + 74 q^{17} + 60 q^{19} - 28 q^{20} + 182 q^{23} - 109 q^{25} - 32 q^{26} - 182 q^{28} - 90 q^{29} - 8 q^{31}+ \cdots - 333 q^{98}+O(q^{100})

q - q^2 - 7 * q^4 + 4 * q^5 + 26 * q^7 + 15 * q^8 - 4 * q^10 + 32 * q^13 - 26 * q^14 + 41 * q^16 + 74 * q^17 + 60 * q^19 - 28 * q^20 + 182 * q^23 - 109 * q^25 - 32 * q^26 - 182 * q^28 - 90 * q^29 - 8 * q^31 - 161 * q^32 - 74 * q^34 + 104 * q^35 - 66 * q^37 - 60 * q^38 + 60 * q^40 + 422 * q^41 - 408 * q^43 - 182 * q^46 + 506 * q^47 + 333 * q^49 + 109 * q^50 - 224 * q^52 - 348 * q^53 + 390 * q^56 + 90 * q^58 + 200 * q^59 - 132 * q^61 + 8 * q^62 - 167 * q^64 + 128 * q^65 - 1036 * q^67 - 518 * q^68 - 104 * q^70 - 762 * q^71 + 542 * q^73 + 66 * q^74 - 420 * q^76 + 550 * q^79 + 164 * q^80 - 422 * q^82 - 132 * q^83 + 296 * q^85 + 408 * q^86 - 570 * q^89 + 832 * q^91 - 1274 * q^92 - 506 * q^94 + 240 * q^95 + 14 * q^97 - 333 * q^98

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

−7.00000

4.00000

26.0000

15.0000

−4.00000

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$11$	$-1$

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	1089.4.a.e		1
3.b	odd	2	1		363.4.a.d		1
11.b	odd	2	1		99.4.a.a		1
33.d	even	2	1		33.4.a.b	✓	1
44.c	even	2	1		1584.4.a.l		1
55.d	odd	2	1		2475.4.a.e		1
132.d	odd	2	1		528.4.a.h		1
165.d	even	2	1		825.4.a.f		1
165.l	odd	4	2		825.4.c.f		2
231.h	odd	2	1		1617.4.a.d		1
264.m	even	2	1		2112.4.a.u		1
264.p	odd	2	1		2112.4.a.h		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
33.4.a.b	✓	1	33.d	even	2	1
99.4.a.a		1	11.b	odd	2	1
363.4.a.d		1	3.b	odd	2	1
528.4.a.h		1	132.d	odd	2	1
825.4.a.f		1	165.d	even	2	1
825.4.c.f		2	165.l	odd	4	2
1089.4.a.e		1	1.a	even	1	1	trivial
1584.4.a.l		1	44.c	even	2	1
1617.4.a.d		1	231.h	odd	2	1
2112.4.a.h		1	264.p	odd	2	1
2112.4.a.u		1	264.m	even	2	1
2475.4.a.e		1	55.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1089))$ :

T_{2} + 1

T2 + 1

T_{5} - 4

T5 - 4

T_{7} - 26

T7 - 26

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$ T + 1
$3$	$T$ T
$5$	$T - 4$ T - 4
$7$	$T - 26$ T - 26
$11$	$T$ T
$13$	$T - 32$ T - 32
$17$	$T - 74$ T - 74
$19$	$T - 60$ T - 60
$23$	$T - 182$ T - 182
$29$	$T + 90$ T + 90
$31$	$T + 8$ T + 8
$37$	$T + 66$ T + 66
$41$	$T - 422$ T - 422
$43$	$T + 408$ T + 408
$47$	$T - 506$ T - 506
$53$	$T + 348$ T + 348
$59$	$T - 200$ T - 200
$61$	$T + 132$ T + 132
$67$	$T + 1036$ T + 1036
$71$	$T + 762$ T + 762
$73$	$T - 542$ T - 542
$79$	$T - 550$ T - 550
$83$	$T + 132$ T + 132
$89$	$T + 570$ T + 570
$97$	$T - 14$ T - 14
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