Properties

Label 833.2.o.g
Level $833$
Weight $2$
Character orbit 833.o
Analytic conductor $6.652$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(30,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.30");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.o (of order \(12\), degree \(4\), not 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: no
Analytic conductor: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 119)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{3} + 24 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 12 q^{12} - 16 q^{16} + 12 q^{17} + 8 q^{18} + 40 q^{20} - 40 q^{22} - 4 q^{24} + 16 q^{27} + 32 q^{29} + 36 q^{30} - 4 q^{31} + 16 q^{33} + 72 q^{34} + 28 q^{37} - 48 q^{38} - 20 q^{39} + 24 q^{40} - 48 q^{41} + 28 q^{44} - 36 q^{45} - 8 q^{46} - 40 q^{47} - 16 q^{48} - 56 q^{50} + 40 q^{51} + 28 q^{54} - 80 q^{55} + 72 q^{57} - 56 q^{58} + 16 q^{61} - 80 q^{62} + 64 q^{64} - 8 q^{65} + 32 q^{68} - 176 q^{69} - 16 q^{71} - 108 q^{72} - 8 q^{73} - 36 q^{74} - 8 q^{75} - 88 q^{78} + 4 q^{79} + 116 q^{80} - 4 q^{81} + 16 q^{82} + 32 q^{85} - 44 q^{86} - 72 q^{88} - 48 q^{89} + 112 q^{90} - 64 q^{92} - 44 q^{95} - 68 q^{96} - 48 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
30.1 −2.17421 1.25528i −0.677398 + 2.52808i 2.15147 + 3.72645i 2.89431 0.775527i 4.64626 4.64626i 0 5.78166i −3.33426 1.92503i −7.26634 1.94701i
30.2 −2.01236 1.16184i 0.545242 2.03487i 1.69972 + 2.94400i 1.42180 0.380969i −3.46141 + 3.46141i 0 3.25185i −1.24533 0.718992i −3.30378 0.885246i
30.3 −1.36164 0.786146i −0.526518 + 1.96499i 0.236050 + 0.408850i −3.27915 + 0.878646i 2.26170 2.26170i 0 2.40230i −0.985896 0.569207i 5.15578 + 1.38149i
30.4 −1.21683 0.702538i 0.166262 0.620497i −0.0128813 0.0223111i −0.286192 + 0.0766850i −0.638235 + 0.638235i 0 2.84635i 2.24070 + 1.29367i 0.402122 + 0.107748i
30.5 −0.107682 0.0621703i −0.445460 + 1.66248i −0.992270 1.71866i 3.11267 0.834039i 0.151325 0.151325i 0 0.495440i 0.0326760 + 0.0188655i −0.387032 0.103705i
30.6 0.504509 + 0.291278i −0.223439 + 0.833886i −0.830314 1.43815i −1.93011 + 0.517173i −0.355620 + 0.355620i 0 2.13252i 1.95264 + 1.12735i −1.12440 0.301282i
30.7 0.615152 + 0.355158i 0.775643 2.89474i −0.747726 1.29510i 3.64268 0.976053i 1.50523 1.50523i 0 2.48287i −5.17981 2.99057i 2.58745 + 0.693306i
30.8 1.63202 + 0.942246i 0.342447 1.27803i 0.775655 + 1.34347i −1.33407 + 0.357462i 1.76310 1.76310i 0 0.845554i 1.08198 + 0.624683i −2.51404 0.673635i
30.9 1.84967 + 1.06791i −0.799375 + 2.98331i 1.28084 + 2.21849i −1.05290 + 0.282125i −4.66447 + 4.66447i 0 1.19966i −5.66305 3.26956i −2.24880 0.602565i
30.10 2.27138 + 1.31138i 0.110545 0.412559i 2.43945 + 4.22526i 2.27508 0.609605i 0.792113 0.792113i 0 7.55071i 2.44009 + 1.40879i 5.96699 + 1.59885i
361.1 −2.17421 + 1.25528i −0.677398 2.52808i 2.15147 3.72645i 2.89431 + 0.775527i 4.64626 + 4.64626i 0 5.78166i −3.33426 + 1.92503i −7.26634 + 1.94701i
361.2 −2.01236 + 1.16184i 0.545242 + 2.03487i 1.69972 2.94400i 1.42180 + 0.380969i −3.46141 3.46141i 0 3.25185i −1.24533 + 0.718992i −3.30378 + 0.885246i
361.3 −1.36164 + 0.786146i −0.526518 1.96499i 0.236050 0.408850i −3.27915 0.878646i 2.26170 + 2.26170i 0 2.40230i −0.985896 + 0.569207i 5.15578 1.38149i
361.4 −1.21683 + 0.702538i 0.166262 + 0.620497i −0.0128813 + 0.0223111i −0.286192 0.0766850i −0.638235 0.638235i 0 2.84635i 2.24070 1.29367i 0.402122 0.107748i
361.5 −0.107682 + 0.0621703i −0.445460 1.66248i −0.992270 + 1.71866i 3.11267 + 0.834039i 0.151325 + 0.151325i 0 0.495440i 0.0326760 0.0188655i −0.387032 + 0.103705i
361.6 0.504509 0.291278i −0.223439 0.833886i −0.830314 + 1.43815i −1.93011 0.517173i −0.355620 0.355620i 0 2.13252i 1.95264 1.12735i −1.12440 + 0.301282i
361.7 0.615152 0.355158i 0.775643 + 2.89474i −0.747726 + 1.29510i 3.64268 + 0.976053i 1.50523 + 1.50523i 0 2.48287i −5.17981 + 2.99057i 2.58745 0.693306i
361.8 1.63202 0.942246i 0.342447 + 1.27803i 0.775655 1.34347i −1.33407 0.357462i 1.76310 + 1.76310i 0 0.845554i 1.08198 0.624683i −2.51404 + 0.673635i
361.9 1.84967 1.06791i −0.799375 2.98331i 1.28084 2.21849i −1.05290 0.282125i −4.66447 4.66447i 0 1.19966i −5.66305 + 3.26956i −2.24880 + 0.602565i
361.10 2.27138 1.31138i 0.110545 + 0.412559i 2.43945 4.22526i 2.27508 + 0.609605i 0.792113 + 0.792113i 0 7.55071i 2.44009 1.40879i 5.96699 1.59885i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 30.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
17.c even 4 1 inner
119.n even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.o.g 40
7.b odd 2 1 833.2.o.f 40
7.c even 3 1 119.2.g.a 20
7.c even 3 1 inner 833.2.o.g 40
7.d odd 6 1 833.2.g.h 20
7.d odd 6 1 833.2.o.f 40
17.c even 4 1 inner 833.2.o.g 40
21.h odd 6 1 1071.2.n.c 20
119.f odd 4 1 833.2.o.f 40
119.m odd 12 1 833.2.g.h 20
119.m odd 12 1 833.2.o.f 40
119.n even 12 1 119.2.g.a 20
119.n even 12 1 inner 833.2.o.g 40
119.q even 24 1 2023.2.a.m 10
119.q even 24 1 2023.2.a.n 10
357.z odd 12 1 1071.2.n.c 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.2.g.a 20 7.c even 3 1
119.2.g.a 20 119.n even 12 1
833.2.g.h 20 7.d odd 6 1
833.2.g.h 20 119.m odd 12 1
833.2.o.f 40 7.b odd 2 1
833.2.o.f 40 7.d odd 6 1
833.2.o.f 40 119.f odd 4 1
833.2.o.f 40 119.m odd 12 1
833.2.o.g 40 1.a even 1 1 trivial
833.2.o.g 40 7.c even 3 1 inner
833.2.o.g 40 17.c even 4 1 inner
833.2.o.g 40 119.n even 12 1 inner
1071.2.n.c 20 21.h odd 6 1
1071.2.n.c 20 357.z odd 12 1
2023.2.a.m 10 119.q even 24 1
2023.2.a.n 10 119.q even 24 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{40} - 32 T_{2}^{38} + 592 T_{2}^{36} - 7424 T_{2}^{34} + 70064 T_{2}^{32} - 514322 T_{2}^{30} + 3023872 T_{2}^{28} - 14348720 T_{2}^{26} + 55422528 T_{2}^{24} - 173395264 T_{2}^{22} + 438238483 T_{2}^{20} + \cdots + 2401 \) Copy content Toggle raw display
\( T_{3}^{40} - 4 T_{3}^{39} + 8 T_{3}^{38} - 32 T_{3}^{37} - 38 T_{3}^{36} + 404 T_{3}^{35} - 800 T_{3}^{34} + 3252 T_{3}^{33} + 2137 T_{3}^{32} - 34108 T_{3}^{31} + 66480 T_{3}^{30} - 270980 T_{3}^{29} + 389802 T_{3}^{28} + \cdots + 9834496 \) Copy content Toggle raw display