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Properties

Label 833.2.o.d
Level $833$
Weight $2$
Character orbit 833.o
Analytic conductor $6.652$
Analytic rank $0$
Dimension $32$
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: \(32\)
Relative dimension: \(8\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{4} + 8 q^{5} + 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{4} + 8 q^{5} + 12 q^{6} + 6 q^{10} - 18 q^{11} - 26 q^{12} - 8 q^{16} - 10 q^{17} - 40 q^{18} + 24 q^{20} + 52 q^{22} - 12 q^{23} - 14 q^{24} - 60 q^{27} - 32 q^{29} - 44 q^{30} + 6 q^{31} + 8 q^{33} + 40 q^{34} - 2 q^{37} + 32 q^{38} + 14 q^{39} - 72 q^{40} - 4 q^{41} + 24 q^{44} + 4 q^{46} + 36 q^{47} - 72 q^{48} - 80 q^{50} - 20 q^{51} - 12 q^{52} + 18 q^{54} - 72 q^{55} - 48 q^{57} + 8 q^{58} + 52 q^{61} - 36 q^{62} + 24 q^{64} - 2 q^{65} - 28 q^{67} - 24 q^{68} + 8 q^{69} + 80 q^{71} + 36 q^{72} + 16 q^{73} + 60 q^{74} + 2 q^{75} + 64 q^{78} - 6 q^{79} - 30 q^{80} + 40 q^{82} + 68 q^{85} - 4 q^{86} + 30 q^{88} - 8 q^{89} + 20 q^{90} - 40 q^{92} - 12 q^{95} + 30 q^{96} + 76 q^{97} - 92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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 −2.24599 − 1.29672i −0.276368 + 1.03142i 2.36298 + 4.09281i −2.34499 + 0.628338i 1.95819 − 1.95819i 0 − 7.06964i 1.61063 + 0.929897i 6.08161 + 1.62956i
30.2 −1.66831 − 0.963197i −0.400286 + 1.49389i 0.855497 + 1.48177i 3.69830 − 0.990956i 2.10671 − 2.10671i 0 0.556738i 0.526601 + 0.304033i −7.12438 − 1.90897i
30.3 −0.472689 − 0.272907i 0.504312 − 1.88212i −0.851044 − 1.47405i 3.48059 − 0.932620i −0.752026 + 0.752026i 0 2.02065i −0.689966 − 0.398352i −1.89975 − 0.509037i
30.4 0.0388613 + 0.0224366i −0.154931 + 0.578211i −0.998993 − 1.73031i −1.19212 + 0.319429i −0.0189939 + 0.0189939i 0 − 0.179402i 2.28775 + 1.32083i −0.0534944 − 0.0143338i
30.5 1.11340 + 0.642823i 0.832471 − 3.10682i −0.173558 − 0.300611i −2.56026 + 0.686021i 2.92401 − 2.92401i 0 − 3.01756i −6.36126 − 3.67268i −3.29159 − 0.881979i
30.6 1.14763 + 0.662584i −0.238518 + 0.890162i −0.121965 − 0.211249i −0.576009 + 0.154341i −0.863538 + 0.863538i 0 − 2.97358i 1.86258 + 1.07536i −0.763309 − 0.204528i
30.7 1.68856 + 0.974893i 0.402964 − 1.50388i 0.900832 + 1.56029i 2.05737 − 0.551271i 2.14656 − 2.14656i 0 − 0.386712i 0.498791 + 0.287977i 4.01143 + 1.07486i
30.8 2.13058 + 1.23009i −0.669644 + 2.49914i 2.02625 + 3.50956i 2.90123 − 0.777383i −4.50090 + 4.50090i 0 5.04951i −3.19922 − 1.84707i 7.13756 + 1.91250i
361.1 −2.24599 + 1.29672i −0.276368 − 1.03142i 2.36298 − 4.09281i −2.34499 − 0.628338i 1.95819 + 1.95819i 0 7.06964i 1.61063 − 0.929897i 6.08161 − 1.62956i
361.2 −1.66831 + 0.963197i −0.400286 − 1.49389i 0.855497 − 1.48177i 3.69830 + 0.990956i 2.10671 + 2.10671i 0 − 0.556738i 0.526601 − 0.304033i −7.12438 + 1.90897i
361.3 −0.472689 + 0.272907i 0.504312 + 1.88212i −0.851044 + 1.47405i 3.48059 + 0.932620i −0.752026 − 0.752026i 0 − 2.02065i −0.689966 + 0.398352i −1.89975 + 0.509037i
361.4 0.0388613 − 0.0224366i −0.154931 − 0.578211i −0.998993 + 1.73031i −1.19212 − 0.319429i −0.0189939 − 0.0189939i 0 0.179402i 2.28775 − 1.32083i −0.0534944 + 0.0143338i
361.5 1.11340 − 0.642823i 0.832471 + 3.10682i −0.173558 + 0.300611i −2.56026 − 0.686021i 2.92401 + 2.92401i 0 3.01756i −6.36126 + 3.67268i −3.29159 + 0.881979i
361.6 1.14763 − 0.662584i −0.238518 − 0.890162i −0.121965 + 0.211249i −0.576009 − 0.154341i −0.863538 − 0.863538i 0 2.97358i 1.86258 − 1.07536i −0.763309 + 0.204528i
361.7 1.68856 − 0.974893i 0.402964 + 1.50388i 0.900832 − 1.56029i 2.05737 + 0.551271i 2.14656 + 2.14656i 0 0.386712i 0.498791 − 0.287977i 4.01143 − 1.07486i
361.8 2.13058 − 1.23009i −0.669644 − 2.49914i 2.02625 − 3.50956i 2.90123 + 0.777383i −4.50090 − 4.50090i 0 − 5.04951i −3.19922 + 1.84707i 7.13756 − 1.91250i
557.1 −2.13058 + 1.23009i 2.49914 − 0.669644i 2.02625 − 3.50956i −0.777383 + 2.90123i −4.50090 + 4.50090i 0 5.04951i 3.19922 − 1.84707i −1.91250 − 7.13756i
557.2 −1.68856 + 0.974893i −1.50388 + 0.402964i 0.900832 − 1.56029i −0.551271 + 2.05737i 2.14656 − 2.14656i 0 − 0.386712i −0.498791 + 0.287977i −1.07486 − 4.01143i
557.3 −1.14763 + 0.662584i 0.890162 − 0.238518i −0.121965 + 0.211249i 0.154341 − 0.576009i −0.863538 + 0.863538i 0 − 2.97358i −1.86258 + 1.07536i 0.204528 + 0.763309i
557.4 −1.11340 + 0.642823i −3.10682 + 0.832471i −0.173558 + 0.300611i 0.686021 − 2.56026i 2.92401 − 2.92401i 0 − 3.01756i 6.36126 − 3.67268i 0.881979 + 3.29159i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 30.8
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.d 32
7.b odd 2 1 119.2.n.b ✓ 32
7.c even 3 1 833.2.g.f 16
7.c even 3 1 inner 833.2.o.d 32
7.d odd 6 1 119.2.n.b ✓ 32
7.d odd 6 1 833.2.g.g 16
17.c even 4 1 inner 833.2.o.d 32
119.f odd 4 1 119.2.n.b ✓ 32
119.m odd 12 1 119.2.n.b ✓ 32
119.m odd 12 1 833.2.g.g 16
119.n even 12 1 833.2.g.f 16
119.n even 12 1 inner 833.2.o.d 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.2.n.b ✓ 32 7.b odd 2 1
119.2.n.b ✓ 32 7.d odd 6 1
119.2.n.b ✓ 32 119.f odd 4 1
119.2.n.b ✓ 32 119.m odd 12 1
833.2.g.f 16 7.c even 3 1
833.2.g.f 16 119.n even 12 1
833.2.g.g 16 7.d odd 6 1
833.2.g.g 16 119.m odd 12 1
833.2.o.d 32 1.a even 1 1 trivial
833.2.o.d 32 7.c even 3 1 inner
833.2.o.d 32 17.c even 4 1 inner
833.2.o.d 32 119.n even 12 1 inner

Hecke kernels

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

\( T_{2}^{32} - 24 T_{2}^{30} + 346 T_{2}^{28} - 3268 T_{2}^{26} + 22889 T_{2}^{24} - 119774 T_{2}^{22} + \cdots + 1 \) Copy content Toggle raw display
\( T_{3}^{32} + 20 T_{3}^{29} - 90 T_{3}^{28} - 72 T_{3}^{27} + 200 T_{3}^{26} - 1216 T_{3}^{25} + \cdots + 279841 \) Copy content Toggle raw display