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 $1$

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

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:

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 \(S_{4}^{\mathrm{new}}(\Gamma_0(833))\):

\( T_{2} + 3 \) Copy content Toggle raw display
\( T_{3} - 8 \) Copy content Toggle raw display

Hecke characteristic polynomials

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