Properties

 Label 833.4.a.a Level $833$ Weight $4$ Character orbit 833.a Self dual yes Analytic conductor $49.149$ Analytic rank $1$ 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] = [833,4,Mod(1,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("833.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$833 = 7^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 833.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: $$49.1485910348$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 17) 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)

 $$f(q)$$ $$=$$ $$q - 3 q^{2} + 8 q^{3} + q^{4} - 6 q^{5} - 24 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10})$$ q - 3 * q^2 + 8 * q^3 + q^4 - 6 * q^5 - 24 * q^6 + 21 * q^8 + 37 * q^9 $$q - 3 q^{2} + 8 q^{3} + q^{4} - 6 q^{5} - 24 q^{6} + 21 q^{8} + 37 q^{9} + 18 q^{10} - 24 q^{11} + 8 q^{12} + 58 q^{13} - 48 q^{15} - 71 q^{16} - 17 q^{17} - 111 q^{18} - 116 q^{19} - 6 q^{20} + 72 q^{22} - 60 q^{23} + 168 q^{24} - 89 q^{25} - 174 q^{26} + 80 q^{27} + 30 q^{29} + 144 q^{30} + 172 q^{31} + 45 q^{32} - 192 q^{33} + 51 q^{34} + 37 q^{36} - 58 q^{37} + 348 q^{38} + 464 q^{39} - 126 q^{40} + 342 q^{41} - 148 q^{43} - 24 q^{44} - 222 q^{45} + 180 q^{46} - 288 q^{47} - 568 q^{48} + 267 q^{50} - 136 q^{51} + 58 q^{52} + 318 q^{53} - 240 q^{54} + 144 q^{55} - 928 q^{57} - 90 q^{58} - 252 q^{59} - 48 q^{60} - 110 q^{61} - 516 q^{62} + 433 q^{64} - 348 q^{65} + 576 q^{66} - 484 q^{67} - 17 q^{68} - 480 q^{69} - 708 q^{71} + 777 q^{72} - 362 q^{73} + 174 q^{74} - 712 q^{75} - 116 q^{76} - 1392 q^{78} - 484 q^{79} + 426 q^{80} - 359 q^{81} - 1026 q^{82} - 756 q^{83} + 102 q^{85} + 444 q^{86} + 240 q^{87} - 504 q^{88} + 774 q^{89} + 666 q^{90} - 60 q^{92} + 1376 q^{93} + 864 q^{94} + 696 q^{95} + 360 q^{96} + 382 q^{97} - 888 q^{99}+O(q^{100})$$ q - 3 * q^2 + 8 * q^3 + q^4 - 6 * q^5 - 24 * q^6 + 21 * q^8 + 37 * q^9 + 18 * q^10 - 24 * q^11 + 8 * q^12 + 58 * q^13 - 48 * q^15 - 71 * q^16 - 17 * q^17 - 111 * q^18 - 116 * q^19 - 6 * q^20 + 72 * q^22 - 60 * q^23 + 168 * q^24 - 89 * q^25 - 174 * q^26 + 80 * q^27 + 30 * q^29 + 144 * q^30 + 172 * q^31 + 45 * q^32 - 192 * q^33 + 51 * q^34 + 37 * q^36 - 58 * q^37 + 348 * q^38 + 464 * q^39 - 126 * q^40 + 342 * q^41 - 148 * q^43 - 24 * q^44 - 222 * q^45 + 180 * q^46 - 288 * q^47 - 568 * q^48 + 267 * q^50 - 136 * q^51 + 58 * q^52 + 318 * q^53 - 240 * q^54 + 144 * q^55 - 928 * q^57 - 90 * q^58 - 252 * q^59 - 48 * q^60 - 110 * q^61 - 516 * q^62 + 433 * q^64 - 348 * q^65 + 576 * q^66 - 484 * q^67 - 17 * q^68 - 480 * q^69 - 708 * q^71 + 777 * q^72 - 362 * q^73 + 174 * q^74 - 712 * q^75 - 116 * q^76 - 1392 * q^78 - 484 * q^79 + 426 * q^80 - 359 * q^81 - 1026 * q^82 - 756 * q^83 + 102 * q^85 + 444 * q^86 + 240 * q^87 - 504 * q^88 + 774 * q^89 + 666 * q^90 - 60 * q^92 + 1376 * q^93 + 864 * q^94 + 696 * q^95 + 360 * q^96 + 382 * q^97 - 888 * 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
−3.00000 8.00000 1.00000 −6.00000 −24.0000 0 21.0000 37.0000 18.0000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$7$$ $$-1$$
$$17$$ $$1$$

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 833.4.a.a 1
7.b odd 2 1 17.4.a.a 1
21.c even 2 1 153.4.a.d 1
28.d even 2 1 272.4.a.d 1
35.c odd 2 1 425.4.a.d 1
35.f even 4 2 425.4.b.c 2
56.e even 2 1 1088.4.a.a 1
56.h odd 2 1 1088.4.a.l 1
77.b even 2 1 2057.4.a.d 1
84.h odd 2 1 2448.4.a.f 1
119.d odd 2 1 289.4.a.a 1
119.f odd 4 2 289.4.b.a 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
17.4.a.a 1 7.b odd 2 1
153.4.a.d 1 21.c even 2 1
272.4.a.d 1 28.d even 2 1
289.4.a.a 1 119.d odd 2 1
289.4.b.a 2 119.f odd 4 2
425.4.a.d 1 35.c odd 2 1
425.4.b.c 2 35.f even 4 2
833.4.a.a 1 1.a even 1 1 trivial
1088.4.a.a 1 56.e even 2 1
1088.4.a.l 1 56.h odd 2 1
2057.4.a.d 1 77.b even 2 1
2448.4.a.f 1 84.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(833))$$:

 $$T_{2} + 3$$ T2 + 3 $$T_{3} - 8$$ T3 - 8

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T + 3$$
$3$ $$T - 8$$
$5$ $$T + 6$$
$7$ $$T$$
$11$ $$T + 24$$
$13$ $$T - 58$$
$17$ $$T + 17$$
$19$ $$T + 116$$
$23$ $$T + 60$$
$29$ $$T - 30$$
$31$ $$T - 172$$
$37$ $$T + 58$$
$41$ $$T - 342$$
$43$ $$T + 148$$
$47$ $$T + 288$$
$53$ $$T - 318$$
$59$ $$T + 252$$
$61$ $$T + 110$$
$67$ $$T + 484$$
$71$ $$T + 708$$
$73$ $$T + 362$$
$79$ $$T + 484$$
$83$ $$T + 756$$
$89$ $$T - 774$$
$97$ $$T - 382$$