Properties

Label 93.3.j.a
Level $93$
Weight $3$
Character orbit 93.j
Analytic conductor $2.534$
Analytic rank $0$
Dimension $40$
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] = [93,3,Mod(46,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.46");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 93.j (of order \(10\), degree \(4\), 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: \(2.53406645855\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 20 q^{4} - 4 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q - 20 q^{4} - 4 q^{7} - 6 q^{8} + 30 q^{9} - 18 q^{10} + 10 q^{11} - 30 q^{13} + 10 q^{14} + 84 q^{16} - 80 q^{17} - 36 q^{19} + 68 q^{20} + 120 q^{21} - 230 q^{22} - 70 q^{23} - 120 q^{24} + 136 q^{25} - 54 q^{28} - 20 q^{29} - 172 q^{31} - 124 q^{32} + 90 q^{33} + 440 q^{34} + 88 q^{35} - 180 q^{36} + 210 q^{38} - 12 q^{39} + 452 q^{40} + 58 q^{41} + 120 q^{42} - 90 q^{43} - 440 q^{44} + 230 q^{46} + 20 q^{47} - 546 q^{49} - 452 q^{50} + 6 q^{51} + 60 q^{52} + 60 q^{53} - 90 q^{54} - 440 q^{55} - 36 q^{56} - 250 q^{58} + 64 q^{59} + 150 q^{60} + 242 q^{62} - 48 q^{63} + 674 q^{64} - 20 q^{65} + 96 q^{66} - 184 q^{67} - 144 q^{69} + 150 q^{70} + 748 q^{71} + 18 q^{72} + 130 q^{73} - 60 q^{74} - 60 q^{75} + 114 q^{76} + 1080 q^{77} + 204 q^{78} - 590 q^{79} - 350 q^{80} - 90 q^{81} + 202 q^{82} - 180 q^{84} - 480 q^{85} - 280 q^{86} - 96 q^{87} + 30 q^{89} + 54 q^{90} + 240 q^{91} - 288 q^{93} - 308 q^{94} + 458 q^{95} + 810 q^{96} + 762 q^{97} + 660 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
46.1 −2.81198 + 2.04302i −1.01807 + 1.40126i 2.49722 7.68566i 8.54726 6.02026i 2.24339 6.90443i 4.38352 + 13.4911i −0.927051 2.85317i −24.0347 + 17.4623i
46.2 −2.30022 + 1.67121i 1.01807 1.40126i 1.26201 3.88406i −2.14190 4.92461i 2.44257 7.51745i 0.0737491 + 0.226976i −0.927051 2.85317i 4.92684 3.57956i
46.3 −1.88421 + 1.36896i −1.01807 + 1.40126i 0.440127 1.35457i −1.03397 4.03396i −2.42647 + 7.46790i −1.85375 5.70527i −0.927051 2.85317i 1.94822 1.41546i
46.4 −0.834306 + 0.606159i −1.01807 + 1.40126i −0.907430 + 2.79278i −6.68474 1.78619i 3.83492 11.8027i −2.21050 6.80322i −0.927051 2.85317i 5.57712 4.05201i
46.5 −0.343439 + 0.249523i 1.01807 1.40126i −1.18038 + 3.63283i −9.35344 0.735280i −3.34669 + 10.3001i −1.02582 3.15714i −0.927051 2.85317i 3.21234 2.33390i
46.6 0.506379 0.367906i 1.01807 1.40126i −1.11500 + 3.43163i 6.13088 1.08412i 0.632043 1.94523i 1.47158 + 4.52905i −0.927051 2.85317i 3.10455 2.25559i
46.7 0.722232 0.524732i −1.01807 + 1.40126i −0.989793 + 3.04627i −0.251341 1.54625i −2.35961 + 7.26213i 1.98709 + 6.11563i −0.927051 2.85317i −0.181527 + 0.131887i
46.8 2.14291 1.55692i −1.01807 + 1.40126i 0.932010 2.86843i 6.01190 4.58783i 1.84262 5.67100i 0.805383 + 2.47872i −0.927051 2.85317i 12.8830 9.36002i
46.9 2.21529 1.60950i 1.01807 1.40126i 1.08094 3.32680i −3.48111 4.74279i 2.48029 7.63354i 0.424767 + 1.30730i −0.927051 2.85317i −7.71166 + 5.60285i
46.10 2.58734 1.87981i 1.01807 1.40126i 1.92457 5.92321i 2.25645 5.53932i −4.10699 + 12.6400i −2.20191 6.77679i −0.927051 2.85317i 5.83820 4.24170i
58.1 −1.18163 3.63669i −1.64728 0.535233i −8.59320 + 6.24332i −0.0151265 6.62309i −3.76145 + 2.73285i 20.4848 + 14.8831i 2.42705 + 1.76336i 0.0178739 + 0.0550103i
58.2 −0.923820 2.84322i 1.64728 + 0.535233i −3.99442 + 2.90211i 8.90434 5.17804i 1.59402 1.15813i 2.26711 + 1.64715i 2.42705 + 1.76336i −8.22601 25.3170i
58.3 −0.481994 1.48342i −1.64728 0.535233i 1.26784 0.921139i 6.42554 2.70159i 0.594204 0.431714i −7.02503 5.10399i 2.42705 + 1.76336i −3.09707 9.53180i
58.4 −0.291155 0.896083i −1.64728 0.535233i 2.51787 1.82934i −8.84927 1.63193i −2.33169 + 1.69407i −5.42135 3.93884i 2.42705 + 1.76336i 2.57651 + 7.92969i
58.5 −0.198592 0.611203i 1.64728 + 0.535233i 2.90194 2.10838i −4.31719 1.11311i 8.23580 5.98366i −3.94463 2.86594i 2.42705 + 1.76336i 0.857359 + 2.63868i
58.6 −0.103278 0.317856i 1.64728 + 0.535233i 3.14570 2.28549i 1.90053 0.578875i −2.74648 + 1.99543i −2.13287 1.54962i 2.42705 + 1.76336i −0.196282 0.604094i
58.7 0.397404 + 1.22308i −1.64728 0.535233i 1.89806 1.37902i 2.24215 2.22746i 3.94472 2.86601i 6.60263 + 4.79709i 2.42705 + 1.76336i 0.891038 + 2.74233i
58.8 0.694084 + 2.13617i 1.64728 + 0.535233i −0.845405 + 0.614223i 2.10985 3.89036i −2.29578 + 1.66798i 5.36967 + 3.90130i 2.42705 + 1.76336i 1.46441 + 4.50700i
58.9 0.928173 + 2.85662i −1.64728 0.535233i −4.06272 + 2.95174i −3.87558 5.20244i −10.7252 + 7.79233i −2.48294 1.80396i 2.42705 + 1.76336i −3.59721 11.0711i
58.10 1.16081 + 3.57260i 1.64728 + 0.535233i −8.17995 + 5.94308i −4.52523 6.50638i 4.25581 3.09203i −18.5715 13.4930i 2.42705 + 1.76336i −5.25293 16.1669i
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 46.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.f odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 93.3.j.a 40
3.b odd 2 1 279.3.v.c 40
31.f odd 10 1 inner 93.3.j.a 40
93.k even 10 1 279.3.v.c 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
93.3.j.a 40 1.a even 1 1 trivial
93.3.j.a 40 31.f odd 10 1 inner
279.3.v.c 40 3.b odd 2 1
279.3.v.c 40 93.k even 10 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(93, [\chi])\).