Properties

 Label 279.1.d.b Level $279$ Weight $1$ Character orbit 279.d Self dual yes Analytic conductor $0.139$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -31 Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,1,Mod(154,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("279.154");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$279 = 3^{2} \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 279.d (of order $$2$$, degree $$1$$, minimal)

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: $$0.139239138525$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 31) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.31.1 Artin image: $D_6$ Artin field: Galois closure of 6.0.25947.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{5} - q^{7} - q^{8}+O(q^{10})$$ q + q^2 + q^5 - q^7 - q^8 $$q + q^{2} + q^{5} - q^{7} - q^{8} + q^{10} - q^{14} - q^{16} - q^{19} + q^{31} - q^{35} - q^{38} - q^{40} + q^{41} - 2 q^{47} + q^{56} + q^{59} + q^{62} + q^{64} + 2 q^{67} - q^{70} + q^{71} - q^{80} + q^{82} - 2 q^{94} - q^{95} - q^{97}+O(q^{100})$$ q + q^2 + q^5 - q^7 - q^8 + q^10 - q^14 - q^16 - q^19 + q^31 - q^35 - q^38 - q^40 + q^41 - 2 * q^47 + q^56 + q^59 + q^62 + q^64 + 2 * q^67 - q^70 + q^71 - q^80 + q^82 - 2 * q^94 - q^95 - q^97

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$218$$ $$\chi(n)$$ $$-1$$ $$1$$

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
154.1
 0
1.00000 0 0 1.00000 0 −1.00000 −1.00000 0 1.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.b odd 2 1 CM by $$\Q(\sqrt{-31})$$

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 279.1.d.b 1
3.b odd 2 1 31.1.b.a 1
9.c even 3 2 2511.1.m.a 2
9.d odd 6 2 2511.1.m.e 2
12.b even 2 1 496.1.e.a 1
15.d odd 2 1 775.1.d.b 1
15.e even 4 2 775.1.c.a 2
21.c even 2 1 1519.1.c.a 1
21.g even 6 2 1519.1.n.a 2
21.h odd 6 2 1519.1.n.b 2
24.f even 2 1 1984.1.e.b 1
24.h odd 2 1 1984.1.e.a 1
31.b odd 2 1 CM 279.1.d.b 1
33.d even 2 1 3751.1.d.b 1
33.f even 10 4 3751.1.t.a 4
33.h odd 10 4 3751.1.t.c 4
93.c even 2 1 31.1.b.a 1
93.g even 6 2 961.1.e.a 2
93.h odd 6 2 961.1.e.a 2
93.k even 10 4 961.1.f.a 4
93.l odd 10 4 961.1.f.a 4
93.o odd 30 8 961.1.h.a 8
93.p even 30 8 961.1.h.a 8
279.m odd 6 2 2511.1.m.a 2
279.s even 6 2 2511.1.m.e 2
372.b odd 2 1 496.1.e.a 1
465.g even 2 1 775.1.d.b 1
465.m odd 4 2 775.1.c.a 2
651.e odd 2 1 1519.1.c.a 1
651.be odd 6 2 1519.1.n.a 2
651.bg even 6 2 1519.1.n.b 2
744.m odd 2 1 1984.1.e.b 1
744.o even 2 1 1984.1.e.a 1
1023.g odd 2 1 3751.1.d.b 1
1023.bg odd 10 4 3751.1.t.a 4
1023.cg even 10 4 3751.1.t.c 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
31.1.b.a 1 3.b odd 2 1
31.1.b.a 1 93.c even 2 1
279.1.d.b 1 1.a even 1 1 trivial
279.1.d.b 1 31.b odd 2 1 CM
496.1.e.a 1 12.b even 2 1
496.1.e.a 1 372.b odd 2 1
775.1.c.a 2 15.e even 4 2
775.1.c.a 2 465.m odd 4 2
775.1.d.b 1 15.d odd 2 1
775.1.d.b 1 465.g even 2 1
961.1.e.a 2 93.g even 6 2
961.1.e.a 2 93.h odd 6 2
961.1.f.a 4 93.k even 10 4
961.1.f.a 4 93.l odd 10 4
961.1.h.a 8 93.o odd 30 8
961.1.h.a 8 93.p even 30 8
1519.1.c.a 1 21.c even 2 1
1519.1.c.a 1 651.e odd 2 1
1519.1.n.a 2 21.g even 6 2
1519.1.n.a 2 651.be odd 6 2
1519.1.n.b 2 21.h odd 6 2
1519.1.n.b 2 651.bg even 6 2
1984.1.e.a 1 24.h odd 2 1
1984.1.e.a 1 744.o even 2 1
1984.1.e.b 1 24.f even 2 1
1984.1.e.b 1 744.m odd 2 1
2511.1.m.a 2 9.c even 3 2
2511.1.m.a 2 279.m odd 6 2
2511.1.m.e 2 9.d odd 6 2
2511.1.m.e 2 279.s even 6 2
3751.1.d.b 1 33.d even 2 1
3751.1.d.b 1 1023.g odd 2 1
3751.1.t.a 4 33.f even 10 4
3751.1.t.a 4 1023.bg odd 10 4
3751.1.t.c 4 33.h odd 10 4
3751.1.t.c 4 1023.cg even 10 4

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2} - 1$$ acting on $$S_{1}^{\mathrm{new}}(279, [\chi])$$.

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T - 1$$
$3$ $$T$$
$5$ $$T - 1$$
$7$ $$T + 1$$
$11$ $$T$$
$13$ $$T$$
$17$ $$T$$
$19$ $$T + 1$$
$23$ $$T$$
$29$ $$T$$
$31$ $$T - 1$$
$37$ $$T$$
$41$ $$T - 1$$
$43$ $$T$$
$47$ $$T + 2$$
$53$ $$T$$
$59$ $$T - 1$$
$61$ $$T$$
$67$ $$T - 2$$
$71$ $$T - 1$$
$73$ $$T$$
$79$ $$T$$
$83$ $$T$$
$89$ $$T$$
$97$ $$T + 1$$