LMFDB - Newform orbit 19.4.a.a

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,4,Mod(1,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("19.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$19$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	19.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$1.12103629011$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
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^{2} - 5 q^{3} + q^{4} - 12 q^{5} + 15 q^{6} + 11 q^{7} + 21 q^{8} - 2 q^{9} + 36 q^{10} - 54 q^{11} - 5 q^{12} + 11 q^{13} - 33 q^{14} + 60 q^{15} - 71 q^{16} - 93 q^{17} + 6 q^{18} + 19 q^{19}+ \cdots + 108 q^{99}+O(q^{100})

q - 3 * q^2 - 5 * q^3 + q^4 - 12 * q^5 + 15 * q^6 + 11 * q^7 + 21 * q^8 - 2 * q^9 + 36 * q^10 - 54 * q^11 - 5 * q^12 + 11 * q^13 - 33 * q^14 + 60 * q^15 - 71 * q^16 - 93 * q^17 + 6 * q^18 + 19 * q^19 - 12 * q^20 - 55 * q^21 + 162 * q^22 + 183 * q^23 - 105 * q^24 + 19 * q^25 - 33 * q^26 + 145 * q^27 + 11 * q^28 - 249 * q^29 - 180 * q^30 + 56 * q^31 + 45 * q^32 + 270 * q^33 + 279 * q^34 - 132 * q^35 - 2 * q^36 - 250 * q^37 - 57 * q^38 - 55 * q^39 - 252 * q^40 + 240 * q^41 + 165 * q^42 - 196 * q^43 - 54 * q^44 + 24 * q^45 - 549 * q^46 - 168 * q^47 + 355 * q^48 - 222 * q^49 - 57 * q^50 + 465 * q^51 + 11 * q^52 + 435 * q^53 - 435 * q^54 + 648 * q^55 + 231 * q^56 - 95 * q^57 + 747 * q^58 + 195 * q^59 + 60 * q^60 - 358 * q^61 - 168 * q^62 - 22 * q^63 + 433 * q^64 - 132 * q^65 - 810 * q^66 - 961 * q^67 - 93 * q^68 - 915 * q^69 + 396 * q^70 - 246 * q^71 - 42 * q^72 + 353 * q^73 + 750 * q^74 - 95 * q^75 + 19 * q^76 - 594 * q^77 + 165 * q^78 - 34 * q^79 + 852 * q^80 - 671 * q^81 - 720 * q^82 + 234 * q^83 - 55 * q^84 + 1116 * q^85 + 588 * q^86 + 1245 * q^87 - 1134 * q^88 - 168 * q^89 - 72 * q^90 + 121 * q^91 + 183 * q^92 - 280 * q^93 + 504 * q^94 - 228 * q^95 - 225 * q^96 + 758 * q^97 + 666 * q^98 + 108 * q^99

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

−5.00000

1.00000

−12.0000

15.0000

11.0000

21.0000

−2.00000

36.0000

Atkin-Lehner signs

$p$	Sign
$19$	$-1$

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	19.4.a.a	✓	1
3.b	odd	2	1		171.4.a.d		1
4.b	odd	2	1		304.4.a.b		1
5.b	even	2	1		475.4.a.e		1
5.c	odd	4	2		475.4.b.c		2
7.b	odd	2	1		931.4.a.a		1
8.b	even	2	1		1216.4.a.f		1
8.d	odd	2	1		1216.4.a.a		1
11.b	odd	2	1		2299.4.a.b		1
19.b	odd	2	1		361.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
19.4.a.a	✓	1	1.a	even	1	1	trivial
171.4.a.d		1	3.b	odd	2	1
304.4.a.b		1	4.b	odd	2	1
361.4.a.b		1	19.b	odd	2	1
475.4.a.e		1	5.b	even	2	1
475.4.b.c		2	5.c	odd	4	2
931.4.a.a		1	7.b	odd	2	1
1216.4.a.a		1	8.d	odd	2	1
1216.4.a.f		1	8.b	even	2	1
2299.4.a.b		1	11.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 3$ T2 + 3 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(19))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 3$ T + 3
$3$	$T + 5$ T + 5
$5$	$T + 12$ T + 12
$7$	$T - 11$ T - 11
$11$	$T + 54$ T + 54
$13$	$T - 11$ T - 11
$17$	$T + 93$ T + 93
$19$	$T - 19$ T - 19
$23$	$T - 183$ T - 183
$29$	$T + 249$ T + 249
$31$	$T - 56$ T - 56
$37$	$T + 250$ T + 250
$41$	$T - 240$ T - 240
$43$	$T + 196$ T + 196
$47$	$T + 168$ T + 168
$53$	$T - 435$ T - 435
$59$	$T - 195$ T - 195
$61$	$T + 358$ T + 358
$67$	$T + 961$ T + 961
$71$	$T + 246$ T + 246
$73$	$T - 353$ T - 353
$79$	$T + 34$ T + 34
$83$	$T - 234$ T - 234
$89$	$T + 168$ T + 168
$97$	$T - 758$ T - 758
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