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Properties

Label 927.2.bi.a
Level $927$
Weight $2$
Character orbit 927.bi
Analytic conductor $7.402$
Analytic rank $0$
Dimension $3264$
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] = [927,2,Mod(95,927)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(927, base_ring=CyclotomicField(102))
 
chi = DirichletCharacter(H, H._module([85, 81]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("927.95");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 927.bi (of order \(102\), degree \(32\), 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: \(3264\)
Relative dimension: \(102\) over \(\Q(\zeta_{102})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{102}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 3264 q - 45 q^{2} - 34 q^{3} - 115 q^{4} - 51 q^{5} - 34 q^{6} - 17 q^{7} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 3264 q - 45 q^{2} - 34 q^{3} - 115 q^{4} - 51 q^{5} - 34 q^{6} - 17 q^{7} - 20 q^{9} - 68 q^{10} - 51 q^{11} - 34 q^{12} - 13 q^{13} - 165 q^{14} - 28 q^{15} + 77 q^{16} - 8 q^{18} - 56 q^{19} - 51 q^{20} - 17 q^{22} - 45 q^{23} - 34 q^{24} + 85 q^{25} - 34 q^{27} - 84 q^{28} - 9 q^{29} - 90 q^{30} - 17 q^{31} - 69 q^{32} - 40 q^{33} - 19 q^{34} - 122 q^{36} - 170 q^{37} - 93 q^{38} + 238 q^{39} - 17 q^{40} - 57 q^{41} - 34 q^{42} - 17 q^{43} - 34 q^{45} - 96 q^{46} + 136 q^{48} + 61 q^{49} + 3 q^{50} - 34 q^{51} - 43 q^{52} - 34 q^{54} + 34 q^{55} - 150 q^{56} + 5 q^{58} - 9 q^{59} - 494 q^{60} + 11 q^{61} - 86 q^{63} + 108 q^{64} - 51 q^{65} - 146 q^{66} - 68 q^{67} - 117 q^{68} - 170 q^{69} - 17 q^{70} - 52 q^{72} - 68 q^{73} - 51 q^{74} - 510 q^{75} + 9 q^{76} - 51 q^{77} - 34 q^{78} - 37 q^{79} - 76 q^{81} - 52 q^{82} + 75 q^{83} - 34 q^{84} - 17 q^{85} - 51 q^{86} - 34 q^{87} - 17 q^{88} - 34 q^{90} + 82 q^{91} - 75 q^{92} + 52 q^{93} + 51 q^{94} - 459 q^{95} - 34 q^{96} - 24 q^{97} - 34 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
95.1 −2.10874 + 1.80666i 0.349934 + 1.69633i 0.875990 − 5.64322i −2.60901 + 0.323066i −3.80262 − 2.94492i 0.0172622 − 0.560286i 5.42451 + 8.76089i −2.75509 + 1.18721i 4.91806 − 5.39486i
95.2 −2.09076 + 1.79125i −0.225395 − 1.71732i 0.855900 − 5.51380i −1.24174 + 0.153761i 3.54740 + 3.18676i −0.0837880 + 2.71953i 5.18842 + 8.37958i −2.89839 + 0.774151i 2.32076 − 2.54575i
95.3 −2.03364 + 1.74232i −1.61992 − 0.613062i 0.793246 − 5.11018i 4.03307 − 0.499402i 4.36250 − 1.57567i −0.0605827 + 1.96635i 4.47086 + 7.22069i 2.24831 + 1.98623i −7.33170 + 8.04249i
95.4 −2.01280 + 1.72446i 1.10598 − 1.33297i 0.770817 − 4.96569i −0.125657 + 0.0155597i 0.0725280 + 4.59023i 0.00708920 − 0.230097i 4.22103 + 6.81719i −0.553603 − 2.94848i 0.226090 − 0.248009i
95.5 −2.01125 + 1.72313i −1.46313 + 0.926953i 0.769149 − 4.95494i 0.417593 − 0.0517092i 1.34546 − 4.38550i 0.0883429 − 2.86738i 4.20260 + 6.78743i 1.28152 − 2.71251i −0.750779 + 0.823566i
95.6 −1.99670 + 1.71067i 1.72762 + 0.123814i 0.753648 − 4.85508i 2.53334 − 0.313696i −3.66135 + 2.70817i 0.104511 − 3.39215i 4.03234 + 6.51245i 2.96934 + 0.427807i −4.52171 + 4.96008i
95.7 −1.97291 + 1.69028i 1.50694 + 0.853890i 0.728523 − 4.69323i 0.817653 − 0.101247i −4.41637 + 0.862514i −0.108240 + 3.51319i 3.76027 + 6.07305i 1.54174 + 2.57352i −1.44202 + 1.58182i
95.8 −1.83059 + 1.56835i −1.30721 − 1.13632i 0.584544 − 3.76570i −3.99512 + 0.494704i 4.17510 + 0.0299690i 0.0802797 − 2.60567i 2.29789 + 3.71123i 0.417571 + 2.97080i 6.53757 − 7.17137i
95.9 −1.81580 + 1.55569i −0.375885 + 1.69077i 0.570204 − 3.67331i 2.16193 − 0.267706i −1.94778 − 3.65487i −0.00898312 + 0.291568i 2.16165 + 3.49119i −2.71742 − 1.27107i −3.50918 + 3.84939i
95.10 −1.78997 + 1.53356i −1.72895 − 0.103623i 0.545429 − 3.51371i −1.57574 + 0.195119i 3.25368 − 2.46596i −0.0996404 + 3.23406i 1.93049 + 3.11785i 2.97852 + 0.358316i 2.52131 − 2.76574i
95.11 −1.78934 + 1.53302i −0.736238 + 1.56779i 0.544830 − 3.50986i 0.631319 − 0.0781742i −1.08606 − 3.93397i −0.146228 + 4.74616i 1.92497 + 3.10893i −1.91591 − 2.30853i −1.00980 + 1.10770i
95.12 −1.75139 + 1.50050i 1.72811 − 0.116727i 0.509083 − 3.27957i −4.00232 + 0.495595i −2.85145 + 2.79746i −0.118770 + 3.85496i 1.60120 + 2.58602i 2.97275 − 0.403436i 6.26598 − 6.87345i
95.13 −1.75031 + 1.49958i 0.502377 − 1.65759i 0.508083 − 3.27313i 4.29124 − 0.531371i 1.60637 + 3.65466i 0.0378940 − 1.22994i 1.59231 + 2.57166i −2.49523 − 1.66547i −6.71418 + 7.36511i
95.14 −1.72037 + 1.47393i 0.703553 + 1.58272i 0.480445 − 3.09508i −2.48468 + 0.307671i −3.54319 − 1.68589i 0.0408832 − 1.32696i 1.35018 + 2.18062i −2.01003 + 2.22706i 3.82110 − 4.19155i
95.15 −1.68913 + 1.44716i 0.772277 − 1.55035i 0.452109 − 2.91253i −1.92346 + 0.238176i 0.939126 + 3.73635i 0.143634 − 4.66199i 1.10936 + 1.79168i −1.80718 − 2.39460i 2.90430 − 3.18586i
95.16 −1.66593 + 1.42728i −0.450066 − 1.67256i 0.431405 − 2.77916i 1.12104 − 0.138815i 3.13698 + 2.14399i −0.00438778 + 0.142416i 0.938249 + 1.51532i −2.59488 + 1.50552i −1.66945 + 1.83130i
95.17 −1.59773 + 1.36885i 1.59388 + 0.677888i 0.372201 − 2.39776i −1.78641 + 0.221206i −3.47452 + 1.09871i 0.0749674 − 2.43324i 0.472350 + 0.762872i 2.08094 + 2.16095i 2.55140 − 2.79875i
95.18 −1.50685 + 1.29099i 1.29960 + 1.14501i 0.297157 − 1.91431i 3.19496 − 0.395622i −3.43649 − 0.0475792i −0.0898124 + 2.91507i −0.0655565 − 0.105877i 0.377926 + 2.97610i −4.30358 + 4.72080i
95.19 −1.49610 + 1.28178i −0.953155 + 1.44620i 0.288575 − 1.85903i −3.69715 + 0.457806i −0.427696 − 3.38540i 0.0724167 − 2.35045i −0.123110 − 0.198830i −1.18299 − 2.75691i 4.94451 − 5.42387i
95.20 −1.46462 + 1.25481i 1.47937 − 0.900820i 0.263784 − 1.69932i −0.833806 + 0.103248i −1.03635 + 3.17569i −0.00598848 + 0.194370i −0.284613 − 0.459666i 1.37705 − 2.66528i 1.09166 − 1.19749i
See next 80 embeddings (of 3264 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 95.102
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.d odd 6 1 inner
103.f odd 34 1 inner
927.bi even 102 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 927.2.bi.a ✓ 3264
9.d odd 6 1 inner 927.2.bi.a ✓ 3264
103.f odd 34 1 inner 927.2.bi.a ✓ 3264
927.bi even 102 1 inner 927.2.bi.a ✓ 3264
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
927.2.bi.a ✓ 3264 1.a even 1 1 trivial
927.2.bi.a ✓ 3264 9.d odd 6 1 inner
927.2.bi.a ✓ 3264 103.f odd 34 1 inner
927.2.bi.a ✓ 3264 927.bi even 102 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(927, [\chi])\).