Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(23,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.j (of order \(6\), degree \(2\), 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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
23.1 | −4.68493 | + | 2.70485i | −4.52492 | − | 7.83739i | 10.6324 | − | 18.4159i | 14.9789i | 42.3979 | + | 24.4784i | −18.3113 | − | 10.5720i | 71.7586i | −27.4498 | + | 47.5444i | −40.5158 | − | 70.1754i | ||||
23.2 | −4.60341 | + | 2.65778i | 3.48806 | + | 6.04150i | 10.1276 | − | 17.5415i | − | 11.0780i | −32.1139 | − | 18.5410i | −13.4565 | − | 7.76914i | 65.1431i | −10.8331 | + | 18.7635i | 29.4429 | + | 50.9966i | |||
23.3 | −4.40125 | + | 2.54106i | 0.865871 | + | 1.49973i | 8.91398 | − | 15.4395i | 8.37251i | −7.62183 | − | 4.40046i | −3.75563 | − | 2.16832i | 49.9469i | 12.0005 | − | 20.7855i | −21.2751 | − | 36.8495i | ||||
23.4 | −4.25281 | + | 2.45536i | −2.48451 | − | 4.30330i | 8.05759 | − | 13.9562i | − | 14.5097i | 21.1323 | + | 12.2007i | 21.5060 | + | 12.4165i | 39.8514i | 1.15443 | − | 1.99953i | 35.6265 | + | 61.7070i | |||
23.5 | −4.05448 | + | 2.34086i | −0.806074 | − | 1.39616i | 6.95923 | − | 12.0537i | − | 5.38645i | 6.53643 | + | 3.77381i | −1.17956 | − | 0.681020i | 27.7085i | 12.2005 | − | 21.1319i | 12.6089 | + | 21.8393i | |||
23.6 | −3.65232 | + | 2.10867i | 4.62634 | + | 8.01306i | 4.89294 | − | 8.47483i | 13.5656i | −33.7937 | − | 19.5108i | 13.5120 | + | 7.80115i | 7.53168i | −29.3061 | + | 50.7597i | −28.6052 | − | 49.5457i | ||||
23.7 | −3.43971 | + | 1.98592i | −0.953208 | − | 1.65100i | 3.88775 | − | 6.73378i | 18.9601i | 6.55752 | + | 3.78599i | 20.6923 | + | 11.9467i | − | 0.891668i | 11.6828 | − | 20.2352i | −37.6533 | − | 65.2174i | |||
23.8 | −3.05274 | + | 1.76250i | −3.30496 | − | 5.72436i | 2.21282 | − | 3.83272i | − | 15.7848i | 20.1784 | + | 11.6500i | −30.7733 | − | 17.7670i | − | 12.5996i | −8.34556 | + | 14.4549i | 27.8208 | + | 48.1870i | ||
23.9 | −2.99291 | + | 1.72796i | 2.70873 | + | 4.69166i | 1.97166 | − | 3.41501i | 9.57590i | −16.2140 | − | 9.36113i | −24.1322 | − | 13.9328i | − | 14.0195i | −1.17444 | + | 2.03419i | −16.5467 | − | 28.6598i | |||
23.10 | −2.76240 | + | 1.59487i | −4.96121 | − | 8.59307i | 1.08722 | − | 1.88313i | 1.24067i | 27.4097 | + | 15.8250i | 23.6555 | + | 13.6575i | − | 18.5820i | −35.7273 | + | 61.8814i | −1.97871 | − | 3.42722i | |||
23.11 | −2.65952 | + | 1.53547i | −2.90866 | − | 5.03795i | 0.715353 | − | 1.23903i | 4.09794i | 15.4713 | + | 8.93234i | −10.5127 | − | 6.06949i | − | 20.1739i | −3.42061 | + | 5.92468i | −6.29227 | − | 10.8985i | |||
23.12 | −2.21820 | + | 1.28068i | 0.591773 | + | 1.02498i | −0.719733 | + | 1.24661i | − | 4.85042i | −2.62534 | − | 1.51574i | 5.49965 | + | 3.17522i | − | 24.1778i | 12.7996 | − | 22.1696i | 6.21183 | + | 10.7592i | ||
23.13 | −1.40127 | + | 0.809025i | 1.16324 | + | 2.01478i | −2.69096 | + | 4.66087i | − | 8.11969i | −3.26002 | − | 1.88217i | −7.84996 | − | 4.53218i | − | 21.6526i | 10.7938 | − | 18.6954i | 6.56903 | + | 11.3779i | ||
23.14 | −0.943417 | + | 0.544682i | −1.41111 | − | 2.44412i | −3.40664 | + | 5.90048i | 21.6301i | 2.66254 | + | 1.53722i | −24.7951 | − | 14.3155i | − | 16.1371i | 9.51752 | − | 16.4848i | −11.7815 | − | 20.4062i | |||
23.15 | −0.753305 | + | 0.434921i | 4.96974 | + | 8.60785i | −3.62169 | + | 6.27295i | − | 11.3907i | −7.48747 | − | 4.32289i | −24.1895 | − | 13.9658i | − | 13.2593i | −35.8967 | + | 62.1749i | 4.95404 | + | 8.58064i | ||
23.16 | −0.737315 | + | 0.425689i | −2.76813 | − | 4.79455i | −3.63758 | + | 6.30047i | 7.50257i | 4.08197 | + | 2.35673i | 7.20298 | + | 4.15864i | − | 13.0049i | −1.82513 | + | 3.16122i | −3.19376 | − | 5.53176i | |||
23.17 | −0.586414 | + | 0.338566i | −2.81095 | − | 4.86870i | −3.77075 | + | 6.53112i | − | 21.4343i | 3.29676 | + | 1.90338i | 9.06253 | + | 5.23226i | − | 10.5236i | −2.30284 | + | 3.98864i | 7.25695 | + | 12.5694i | ||
23.18 | −0.575952 | + | 0.332526i | 1.60738 | + | 2.78407i | −3.77885 | + | 6.54517i | 10.5229i | −1.85155 | − | 1.06899i | 25.1101 | + | 14.4973i | − | 10.3467i | 8.33263 | − | 14.4325i | −3.49915 | − | 6.06070i | |||
23.19 | −0.204845 | + | 0.118267i | 3.87126 | + | 6.70523i | −3.97203 | + | 6.87975i | 11.7890i | −1.58602 | − | 0.915689i | 4.94948 | + | 2.85759i | − | 3.77132i | −16.4734 | + | 28.5327i | −1.39425 | − | 2.41491i | |||
23.20 | 0.200845 | − | 0.115958i | −4.34402 | − | 7.52406i | −3.97311 | + | 6.88162i | − | 0.297636i | −1.74495 | − | 1.00745i | −6.82685 | − | 3.94148i | 3.69817i | −24.2410 | + | 41.9867i | −0.0345132 | − | 0.0597786i | |||
See all 72 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.e | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 143.4.j.a | ✓ | 72 |
13.e | even | 6 | 1 | inner | 143.4.j.a | ✓ | 72 |
13.f | odd | 12 | 1 | 1859.4.a.l | 36 | ||
13.f | odd | 12 | 1 | 1859.4.a.m | 36 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
143.4.j.a | ✓ | 72 | 1.a | even | 1 | 1 | trivial |
143.4.j.a | ✓ | 72 | 13.e | even | 6 | 1 | inner |
1859.4.a.l | 36 | 13.f | odd | 12 | 1 | ||
1859.4.a.m | 36 | 13.f | odd | 12 | 1 |
Hecke kernels
This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(143, [\chi])\).