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Properties

Label 833.2.bc.f
Level $833$
Weight $2$
Character orbit 833.bc
Analytic conductor $6.652$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(31,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(48))
 
chi = DirichletCharacter(H, H._module([8, 27]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bc (of order \(48\), degree \(16\), 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: \(160\)
Relative dimension: \(10\) over \(\Q(\zeta_{48})\)
Twist minimal: no (minimal twist has level 119)
Sato-Tate group: $\mathrm{SU}(2)[C_{48}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 160 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 128 q^{15} - 32 q^{18} - 96 q^{22} + 16 q^{23} - 32 q^{29} - 112 q^{30} - 16 q^{32} - 96 q^{36} - 48 q^{37} - 32 q^{43} + 16 q^{44} - 16 q^{46} + 48 q^{51} - 16 q^{53} - 32 q^{57} + 48 q^{58} - 48 q^{60} + 96 q^{64} + 32 q^{65} + 32 q^{71} + 80 q^{72} + 80 q^{74} + 224 q^{78} + 16 q^{79} + 64 q^{81} + 224 q^{85} - 48 q^{86} + 112 q^{88} + 512 q^{92} - 48 q^{93} + 48 q^{95} + 256 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −1.53936 − 1.18119i −0.388001 + 0.442430i 0.456779 + 1.70472i −0.520699 + 1.05587i 1.11987 − 0.222756i 0 −0.174601 + 0.421523i 0.346379 + 2.63101i 2.04873 − 1.01032i
31.2 −1.53936 − 1.18119i 0.388001 − 0.442430i 0.456779 + 1.70472i 0.520699 − 1.05587i −1.11987 + 0.222756i 0 −0.174601 + 0.421523i 0.346379 + 2.63101i −2.04873 + 1.01032i
31.3 −0.265771 − 0.203934i −1.66409 + 1.89753i −0.488593 − 1.82345i −0.891574 + 1.80793i 0.829238 − 0.164946i 0 −0.498405 + 1.20326i −0.439851 − 3.34100i 0.605653 − 0.298675i
31.4 −0.265771 − 0.203934i 1.66409 − 1.89753i −0.488593 − 1.82345i 0.891574 − 1.80793i −0.829238 + 0.164946i 0 −0.498405 + 1.20326i −0.439851 − 3.34100i −0.605653 + 0.298675i
31.5 0.0250379 + 0.0192123i −1.02284 + 1.16632i −0.517380 − 1.93089i 1.30358 − 2.64340i −0.0480174 + 0.00955125i 0 0.0482973 − 0.116600i 0.0774677 + 0.588425i 0.0834247 − 0.0411405i
31.6 0.0250379 + 0.0192123i 1.02284 − 1.16632i −0.517380 − 1.93089i −1.30358 + 2.64340i 0.0480174 − 0.00955125i 0 0.0482973 − 0.116600i 0.0774677 + 0.588425i −0.0834247 + 0.0411405i
31.7 1.29714 + 0.995328i −1.25501 + 1.43107i 0.174248 + 0.650304i 0.255684 − 0.518476i −3.05231 + 0.607142i 0 0.830138 − 2.00413i −0.0813210 − 0.617694i 0.847712 − 0.418045i
31.8 1.29714 + 0.995328i 1.25501 − 1.43107i 0.174248 + 0.650304i −0.255684 + 0.518476i 3.05231 − 0.607142i 0 0.830138 − 2.00413i −0.0813210 − 0.617694i −0.847712 + 0.418045i
31.9 1.94888 + 1.49543i −0.930679 + 1.06124i 1.04420 + 3.89700i −1.67591 + 3.39840i −3.40079 + 0.676459i 0 −1.91254 + 4.61727i 0.131520 + 0.998995i −8.34823 + 4.11689i
31.10 1.94888 + 1.49543i 0.930679 − 1.06124i 1.04420 + 3.89700i 1.67591 − 3.39840i 3.40079 − 0.676459i 0 −1.91254 + 4.61727i 0.131520 + 0.998995i 8.34823 − 4.11689i
80.1 −1.56889 + 2.04462i −2.71574 + 0.177999i −1.20141 − 4.48374i 2.58764 − 0.878387i 3.89676 − 5.83192i 0 6.29042 + 2.60558i 4.36922 − 0.575218i −2.26377 + 6.66885i
80.2 −1.56889 + 2.04462i 2.71574 − 0.177999i −1.20141 − 4.48374i −2.58764 + 0.878387i −3.89676 + 5.83192i 0 6.29042 + 2.60558i 4.36922 − 0.575218i 2.26377 − 6.66885i
80.3 −0.724673 + 0.944412i −0.967822 + 0.0634344i 0.150875 + 0.563072i −0.741562 + 0.251726i 0.641446 − 0.959991i 0 −2.84069 − 1.17665i −2.04168 + 0.268792i 0.299656 − 0.882759i
80.4 −0.724673 + 0.944412i 0.967822 − 0.0634344i 0.150875 + 0.563072i 0.741562 − 0.251726i −0.641446 + 0.959991i 0 −2.84069 − 1.17665i −2.04168 + 0.268792i −0.299656 + 0.882759i
80.5 −0.289073 + 0.376727i −3.01731 + 0.197765i 0.459278 + 1.71405i −0.610635 + 0.207283i 0.797718 − 1.19387i 0 −1.65591 − 0.685900i 6.09072 − 0.801858i 0.0984289 − 0.289962i
80.6 −0.289073 + 0.376727i 3.01731 − 0.197765i 0.459278 + 1.71405i 0.610635 − 0.207283i −0.797718 + 1.19387i 0 −1.65591 − 0.685900i 6.09072 − 0.801858i −0.0984289 + 0.289962i
80.7 0.610037 − 0.795016i −0.718354 + 0.0470834i 0.257733 + 0.961873i 3.02536 − 1.02697i −0.400790 + 0.599825i 0 2.77356 + 1.14885i −2.46052 + 0.323934i 1.02912 − 3.03170i
80.8 0.610037 − 0.795016i 0.718354 − 0.0470834i 0.257733 + 0.961873i −3.02536 + 1.02697i 0.400790 − 0.599825i 0 2.77356 + 1.14885i −2.46052 + 0.323934i −1.02912 + 3.03170i
80.9 1.50668 − 1.96354i −1.47009 + 0.0963546i −1.06777 − 3.98498i −2.00148 + 0.679410i −2.02575 + 3.03175i 0 −4.86028 − 2.01319i −0.822464 + 0.108279i −1.68153 + 4.95363i
80.10 1.50668 − 1.96354i 1.47009 − 0.0963546i −1.06777 − 3.98498i 2.00148 − 0.679410i 2.02575 − 3.03175i 0 −4.86028 − 2.01319i −0.822464 + 0.108279i 1.68153 − 4.95363i
See next 80 embeddings (of 160 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
7.c even 3 1 inner
7.d odd 6 1 inner
17.e odd 16 1 inner
119.p even 16 1 inner
119.s even 48 1 inner
119.t odd 48 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.bc.f 160
7.b odd 2 1 inner 833.2.bc.f 160
7.c even 3 1 119.2.p.a ✓ 80
7.c even 3 1 inner 833.2.bc.f 160
7.d odd 6 1 119.2.p.a ✓ 80
7.d odd 6 1 inner 833.2.bc.f 160
17.e odd 16 1 inner 833.2.bc.f 160
119.p even 16 1 inner 833.2.bc.f 160
119.s even 48 1 119.2.p.a ✓ 80
119.s even 48 1 inner 833.2.bc.f 160
119.t odd 48 1 119.2.p.a ✓ 80
119.t odd 48 1 inner 833.2.bc.f 160
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.2.p.a ✓ 80 7.c even 3 1
119.2.p.a ✓ 80 7.d odd 6 1
119.2.p.a ✓ 80 119.s even 48 1
119.2.p.a ✓ 80 119.t odd 48 1
833.2.bc.f 160 1.a even 1 1 trivial
833.2.bc.f 160 7.b odd 2 1 inner
833.2.bc.f 160 7.c even 3 1 inner
833.2.bc.f 160 7.d odd 6 1 inner
833.2.bc.f 160 17.e odd 16 1 inner
833.2.bc.f 160 119.p even 16 1 inner
833.2.bc.f 160 119.s even 48 1 inner
833.2.bc.f 160 119.t odd 48 1 inner

Hecke kernels

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

\( T_{2}^{80} - 8 T_{2}^{79} + 28 T_{2}^{78} - 48 T_{2}^{77} + 8 T_{2}^{76} + 168 T_{2}^{75} - 616 T_{2}^{74} + \cdots + 1 \) Copy content Toggle raw display
\( T_{3}^{160} - 8 T_{3}^{158} - 20 T_{3}^{156} + 240 T_{3}^{154} + 584 T_{3}^{152} - 4152 T_{3}^{150} + \cdots + 19\!\cdots\!76 \) Copy content Toggle raw display