Properties

Label 927.2.u.c
Level $927$
Weight $2$
Character orbit 927.u
Analytic conductor $7.402$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [927,2,Mod(64,927)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(927, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([0, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("927.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 927.u (of order \(17\), degree \(16\), 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: \(7.40213226737\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(10\) over \(\Q(\zeta_{17})\)
Twist minimal: no (minimal twist has level 309)
Sato-Tate group: $\mathrm{SU}(2)[C_{17}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q + q^{2} - 17 q^{4} + 4 q^{5} - 12 q^{7} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 160 q + q^{2} - 17 q^{4} + 4 q^{5} - 12 q^{7} - 36 q^{8} + 12 q^{10} - q^{11} - 18 q^{13} - 31 q^{14} - 39 q^{16} + 14 q^{17} - 11 q^{19} - 31 q^{20} - 3 q^{23} - 8 q^{25} + 33 q^{26} - 2 q^{28} + 28 q^{29} - 20 q^{31} + 46 q^{32} + 5 q^{34} + 3 q^{35} - 34 q^{37} + 14 q^{38} - 56 q^{40} - 40 q^{41} - 42 q^{43} + 26 q^{44} + 112 q^{46} + 40 q^{47} + 30 q^{49} + 10 q^{50} - 58 q^{52} + 48 q^{53} - 64 q^{55} - 86 q^{56} - 36 q^{58} - 76 q^{59} - 28 q^{61} + 66 q^{62} + 88 q^{64} + 14 q^{65} - 84 q^{67} + 107 q^{68} + 8 q^{70} - 41 q^{71} - 32 q^{73} - 3 q^{74} - 68 q^{76} - 93 q^{77} - 100 q^{79} + 168 q^{80} + 99 q^{82} + 28 q^{83} + 15 q^{85} - 64 q^{86} - 25 q^{88} + 19 q^{89} + 122 q^{91} + 78 q^{92} + 138 q^{94} + 15 q^{95} + 161 q^{97} - 65 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −2.49948 + 0.968304i 0 3.83178 3.49313i 0.0773462 0.271844i 0 −0.232369 0.466661i −3.80546 + 7.64239i 0 0.0699020 + 0.754363i
64.2 −1.73611 + 0.672573i 0 1.08371 0.987928i −0.676537 + 2.37778i 0 −1.91897 3.85381i 0.442804 0.889271i 0 −0.424688 4.58311i
64.3 −1.71741 + 0.665328i 0 1.02881 0.937888i 0.534098 1.87716i 0 1.95172 + 3.91958i 0.499012 1.00215i 0 0.331662 + 3.57920i
64.4 −1.38846 + 0.537892i 0 0.160475 0.146293i 1.13758 3.99817i 0 −1.23948 2.48920i 1.18329 2.37637i 0 0.571105 + 6.16320i
64.5 −0.262893 + 0.101845i 0 −1.41928 + 1.29384i −0.786090 + 2.76282i 0 1.07742 + 2.16375i 0.492682 0.989439i 0 −0.0747227 0.806386i
64.6 −0.00409075 + 0.00158477i 0 −1.47800 + 1.34738i −0.145145 + 0.510132i 0 −0.617079 1.23926i 0.00782178 0.0157082i 0 −0.000214687 0.00231684i
64.7 1.04652 0.405425i 0 −0.547177 + 0.498818i 0.339236 1.19229i 0 −2.16351 4.34491i −1.37091 + 2.75317i 0 −0.128366 1.38529i
64.8 1.20137 0.465414i 0 −0.251333 + 0.229120i 0.761130 2.67509i 0 1.66824 + 3.35029i −1.34386 + 2.69884i 0 −0.330626 3.56802i
64.9 2.06025 0.798145i 0 2.12957 1.94136i −1.07558 + 3.78027i 0 −1.16595 2.34153i 0.868291 1.74376i 0 0.801241 + 8.64677i
64.10 2.36783 0.917302i 0 3.28715 2.99663i 0.482408 1.69549i 0 −0.510982 1.02619i 2.77086 5.56464i 0 −0.413014 4.45713i
100.1 −2.16143 + 1.33830i 0 1.98927 3.99498i 1.14272 0.442694i 0 −0.0140028 + 0.151114i 0.577702 + 6.23440i 0 −1.87746 + 2.48616i
100.2 −1.72168 + 1.06602i 0 0.936298 1.88034i −2.90685 + 1.12612i 0 −0.0148655 + 0.160425i 0.0187880 + 0.202755i 0 3.80419 5.03756i
100.3 −0.953159 + 0.590171i 0 −0.331266 + 0.665272i 3.48587 1.35043i 0 −0.264645 + 2.85597i −0.283755 3.06220i 0 −2.52561 + 3.34444i
100.4 −0.667646 + 0.413389i 0 −0.616616 + 1.23833i −2.23396 + 0.865439i 0 −0.442411 + 4.77438i −0.245142 2.64550i 0 1.13373 1.50130i
100.5 −0.264688 + 0.163888i 0 −0.848276 + 1.70357i 0.994818 0.385395i 0 0.417912 4.50998i −0.112115 1.20992i 0 −0.200155 + 0.265049i
100.6 0.143121 0.0886169i 0 −0.878846 + 1.76496i 1.12462 0.435681i 0 0.127254 1.37329i 0.0616878 + 0.665718i 0 0.122349 0.162016i
100.7 0.745642 0.461682i 0 −0.548645 + 1.10183i −3.51280 + 1.36087i 0 0.144256 1.55677i 0.261440 + 2.82139i 0 −1.99100 + 2.63651i
100.8 1.41641 0.877007i 0 0.345612 0.694083i −0.0873501 + 0.0338396i 0 −0.260165 + 2.80763i 0.188243 + 2.03146i 0 −0.0940463 + 0.124537i
100.9 1.97558 1.22323i 0 1.51515 3.04284i 3.44575 1.33489i 0 0.0397289 0.428743i −0.299983 3.23733i 0 5.17448 6.85212i
100.10 2.33806 1.44767i 0 2.47932 4.97915i −2.45619 + 0.951533i 0 0.0680790 0.734689i −0.903874 9.75436i 0 −4.36522 + 5.78049i
See next 80 embeddings (of 160 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 64.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
103.e even 17 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 927.2.u.c 160
3.b odd 2 1 309.2.i.b 160
103.e even 17 1 inner 927.2.u.c 160
309.l odd 34 1 309.2.i.b 160
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
309.2.i.b 160 3.b odd 2 1
309.2.i.b 160 309.l odd 34 1
927.2.u.c 160 1.a even 1 1 trivial
927.2.u.c 160 103.e even 17 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{160} - T_{2}^{159} + 19 T_{2}^{158} - 8 T_{2}^{157} + 225 T_{2}^{156} - 64 T_{2}^{155} + 1988 T_{2}^{154} + 93 T_{2}^{153} + 14949 T_{2}^{152} + 2922 T_{2}^{151} + 108021 T_{2}^{150} + 34747 T_{2}^{149} + 758906 T_{2}^{148} + \cdots + 8447875949529 \) acting on \(S_{2}^{\mathrm{new}}(927, [\chi])\). Copy content Toggle raw display