Properties

Label 833.4.a.b
Level $833$
Weight $4$
Character orbit 833.a
Self dual yes
Analytic conductor $49.149$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 119)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + 6 q^{3} - 7 q^{4} + 20 q^{5} - 6 q^{6} + 15 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + 6 q^{3} - 7 q^{4} + 20 q^{5} - 6 q^{6} + 15 q^{8} + 9 q^{9} - 20 q^{10} + 60 q^{11} - 42 q^{12} + 68 q^{13} + 120 q^{15} + 41 q^{16} + 17 q^{17} - 9 q^{18} + 70 q^{19} - 140 q^{20} - 60 q^{22} - 176 q^{23} + 90 q^{24} + 275 q^{25} - 68 q^{26} - 108 q^{27} - 90 q^{29} - 120 q^{30} - 196 q^{31} - 161 q^{32} + 360 q^{33} - 17 q^{34} - 63 q^{36} + 22 q^{37} - 70 q^{38} + 408 q^{39} + 300 q^{40} + 138 q^{41} + 328 q^{43} - 420 q^{44} + 180 q^{45} + 176 q^{46} + 12 q^{47} + 246 q^{48} - 275 q^{50} + 102 q^{51} - 476 q^{52} - 234 q^{53} + 108 q^{54} + 1200 q^{55} + 420 q^{57} + 90 q^{58} + 54 q^{59} - 840 q^{60} - 44 q^{61} + 196 q^{62} - 167 q^{64} + 1360 q^{65} - 360 q^{66} - 596 q^{67} - 119 q^{68} - 1056 q^{69} + 200 q^{71} + 135 q^{72} - 1122 q^{73} - 22 q^{74} + 1650 q^{75} - 490 q^{76} - 408 q^{78} + 480 q^{79} + 820 q^{80} - 891 q^{81} - 138 q^{82} + 838 q^{83} + 340 q^{85} - 328 q^{86} - 540 q^{87} + 900 q^{88} - 778 q^{89} - 180 q^{90} + 1232 q^{92} - 1176 q^{93} - 12 q^{94} + 1400 q^{95} - 966 q^{96} - 1142 q^{97} + 540 q^{99}+O(q^{100}) \) 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
−1.00000 6.00000 −7.00000 20.0000 −6.00000 0 15.0000 9.00000 −20.0000
\(n\): 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.b 1
7.b odd 2 1 119.4.a.a 1
21.c even 2 1 1071.4.a.b 1
28.d even 2 1 1904.4.a.a 1
119.d odd 2 1 2023.4.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.4.a.a 1 7.b odd 2 1
833.4.a.b 1 1.a even 1 1 trivial
1071.4.a.b 1 21.c even 2 1
1904.4.a.a 1 28.d even 2 1
2023.4.a.b 1 119.d odd 2 1

Hecke kernels

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

\( T_{2} + 1 \) Copy content Toggle raw display
\( T_{3} - 6 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T - 6 \) Copy content Toggle raw display
$5$ \( T - 20 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 60 \) Copy content Toggle raw display
$13$ \( T - 68 \) Copy content Toggle raw display
$17$ \( T - 17 \) Copy content Toggle raw display
$19$ \( T - 70 \) Copy content Toggle raw display
$23$ \( T + 176 \) Copy content Toggle raw display
$29$ \( T + 90 \) Copy content Toggle raw display
$31$ \( T + 196 \) Copy content Toggle raw display
$37$ \( T - 22 \) Copy content Toggle raw display
$41$ \( T - 138 \) Copy content Toggle raw display
$43$ \( T - 328 \) Copy content Toggle raw display
$47$ \( T - 12 \) Copy content Toggle raw display
$53$ \( T + 234 \) Copy content Toggle raw display
$59$ \( T - 54 \) Copy content Toggle raw display
$61$ \( T + 44 \) Copy content Toggle raw display
$67$ \( T + 596 \) Copy content Toggle raw display
$71$ \( T - 200 \) Copy content Toggle raw display
$73$ \( T + 1122 \) Copy content Toggle raw display
$79$ \( T - 480 \) Copy content Toggle raw display
$83$ \( T - 838 \) Copy content Toggle raw display
$89$ \( T + 778 \) Copy content Toggle raw display
$97$ \( T + 1142 \) Copy content Toggle raw display
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