Properties

 Label 832.4.a.d Level $832$ Weight $4$ Character orbit 832.a Self dual yes Analytic conductor $49.090$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,4,Mod(1,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("832.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$832 = 2^{6} \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 832.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: $$49.0895891248$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 26) 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)

 $$f(q)$$ $$=$$ $$q - 4 q^{3} + 18 q^{5} + 20 q^{7} - 11 q^{9}+O(q^{10})$$ q - 4 * q^3 + 18 * q^5 + 20 * q^7 - 11 * q^9 $$q - 4 q^{3} + 18 q^{5} + 20 q^{7} - 11 q^{9} + 48 q^{11} - 13 q^{13} - 72 q^{15} + 66 q^{17} + 16 q^{19} - 80 q^{21} + 168 q^{23} + 199 q^{25} + 152 q^{27} - 6 q^{29} + 20 q^{31} - 192 q^{33} + 360 q^{35} - 254 q^{37} + 52 q^{39} - 390 q^{41} + 124 q^{43} - 198 q^{45} - 468 q^{47} + 57 q^{49} - 264 q^{51} - 558 q^{53} + 864 q^{55} - 64 q^{57} + 96 q^{59} + 826 q^{61} - 220 q^{63} - 234 q^{65} + 160 q^{67} - 672 q^{69} - 420 q^{71} + 362 q^{73} - 796 q^{75} + 960 q^{77} + 776 q^{79} - 311 q^{81} + 1188 q^{85} + 24 q^{87} + 1626 q^{89} - 260 q^{91} - 80 q^{93} + 288 q^{95} - 1294 q^{97} - 528 q^{99}+O(q^{100})$$ q - 4 * q^3 + 18 * q^5 + 20 * q^7 - 11 * q^9 + 48 * q^11 - 13 * q^13 - 72 * q^15 + 66 * q^17 + 16 * q^19 - 80 * q^21 + 168 * q^23 + 199 * q^25 + 152 * q^27 - 6 * q^29 + 20 * q^31 - 192 * q^33 + 360 * q^35 - 254 * q^37 + 52 * q^39 - 390 * q^41 + 124 * q^43 - 198 * q^45 - 468 * q^47 + 57 * q^49 - 264 * q^51 - 558 * q^53 + 864 * q^55 - 64 * q^57 + 96 * q^59 + 826 * q^61 - 220 * q^63 - 234 * q^65 + 160 * q^67 - 672 * q^69 - 420 * q^71 + 362 * q^73 - 796 * q^75 + 960 * q^77 + 776 * q^79 - 311 * q^81 + 1188 * q^85 + 24 * q^87 + 1626 * q^89 - 260 * q^91 - 80 * q^93 + 288 * q^95 - 1294 * q^97 - 528 * 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
 0
0 −4.00000 0 18.0000 0 20.0000 0 −11.0000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$+1$$
$$13$$ $$+1$$

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 832.4.a.d 1
4.b odd 2 1 832.4.a.o 1
8.b even 2 1 26.4.a.c 1
8.d odd 2 1 208.4.a.b 1
24.f even 2 1 1872.4.a.q 1
24.h odd 2 1 234.4.a.e 1
40.f even 2 1 650.4.a.b 1
40.i odd 4 2 650.4.b.f 2
56.h odd 2 1 1274.4.a.d 1
104.e even 2 1 338.4.a.c 1
104.j odd 4 2 338.4.b.d 2
104.r even 6 2 338.4.c.a 2
104.s even 6 2 338.4.c.e 2
104.x odd 12 4 338.4.e.a 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
26.4.a.c 1 8.b even 2 1
208.4.a.b 1 8.d odd 2 1
234.4.a.e 1 24.h odd 2 1
338.4.a.c 1 104.e even 2 1
338.4.b.d 2 104.j odd 4 2
338.4.c.a 2 104.r even 6 2
338.4.c.e 2 104.s even 6 2
338.4.e.a 4 104.x odd 12 4
650.4.a.b 1 40.f even 2 1
650.4.b.f 2 40.i odd 4 2
832.4.a.d 1 1.a even 1 1 trivial
832.4.a.o 1 4.b odd 2 1
1274.4.a.d 1 56.h odd 2 1
1872.4.a.q 1 24.f even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(832))$$:

 $$T_{3} + 4$$ T3 + 4 $$T_{5} - 18$$ T5 - 18

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T + 4$$
$5$ $$T - 18$$
$7$ $$T - 20$$
$11$ $$T - 48$$
$13$ $$T + 13$$
$17$ $$T - 66$$
$19$ $$T - 16$$
$23$ $$T - 168$$
$29$ $$T + 6$$
$31$ $$T - 20$$
$37$ $$T + 254$$
$41$ $$T + 390$$
$43$ $$T - 124$$
$47$ $$T + 468$$
$53$ $$T + 558$$
$59$ $$T - 96$$
$61$ $$T - 826$$
$67$ $$T - 160$$
$71$ $$T + 420$$
$73$ $$T - 362$$
$79$ $$T - 776$$
$83$ $$T$$
$89$ $$T - 1626$$
$97$ $$T + 1294$$