Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(12,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.12");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.b (of order \(2\), degree \(1\), 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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
12.1 | − | 5.51522i | 3.00574 | −22.4176 | 18.8802i | − | 16.5773i | 0.324979i | 79.5165i | −17.9655 | 104.128 | ||||||||||||||||
12.2 | − | 5.22956i | 1.03843 | −19.3483 | − | 12.1782i | − | 5.43054i | 36.1879i | 59.3469i | −25.9217 | −63.6866 | |||||||||||||||
12.3 | − | 4.98751i | −4.47034 | −16.8752 | − | 20.1605i | 22.2959i | − | 23.8481i | 44.2654i | −7.01607 | −100.551 | |||||||||||||||
12.4 | − | 4.83238i | 9.74664 | −15.3519 | − | 8.44122i | − | 47.0995i | − | 12.5767i | 35.5272i | 67.9971 | −40.7912 | ||||||||||||||
12.5 | − | 4.83029i | −7.08819 | −15.3317 | 9.07266i | 34.2380i | − | 2.15508i | 35.4141i | 23.2424 | 43.8235 | ||||||||||||||||
12.6 | − | 4.27424i | 4.33951 | −10.2691 | 0.295728i | − | 18.5481i | − | 11.5737i | 9.69883i | −8.16862 | 1.26401 | |||||||||||||||
12.7 | − | 3.98165i | −8.48796 | −7.85352 | − | 2.25841i | 33.7961i | 28.5605i | − | 0.583227i | 45.0454 | −8.99219 | |||||||||||||||
12.8 | − | 3.97618i | −1.00306 | −7.81003 | 0.345299i | 3.98837i | − | 17.7538i | − | 0.755338i | −25.9939 | 1.37297 | |||||||||||||||
12.9 | − | 3.37885i | 7.92479 | −3.41661 | 15.9579i | − | 26.7767i | 29.7230i | − | 15.4866i | 35.8023 | 53.9193 | |||||||||||||||
12.10 | − | 2.40428i | 7.21858 | 2.21943 | − | 9.84845i | − | 17.3555i | 8.26104i | − | 24.5704i | 25.1078 | −23.6784 | ||||||||||||||
12.11 | − | 2.37174i | −6.00967 | 2.37485 | 22.0017i | 14.2534i | − | 21.9243i | − | 24.6064i | 9.11608 | 52.1824 | |||||||||||||||
12.12 | − | 2.32803i | −4.42417 | 2.58028 | − | 12.1881i | 10.2996i | 11.2388i | − | 24.6312i | −7.42671 | −28.3743 | |||||||||||||||
12.13 | − | 2.22320i | 2.89827 | 3.05739 | − | 19.1319i | − | 6.44342i | 4.29594i | − | 24.5828i | −18.6000 | −42.5339 | ||||||||||||||
12.14 | − | 2.18512i | −9.62593 | 3.22525 | − | 10.6961i | 21.0338i | − | 26.7047i | − | 24.5285i | 65.6585 | −23.3723 | ||||||||||||||
12.15 | − | 1.26989i | 3.96847 | 6.38737 | 4.99906i | − | 5.03953i | − | 32.3730i | − | 18.2704i | −11.2513 | 6.34827 | ||||||||||||||
12.16 | − | 0.901974i | 8.17246 | 7.18644 | 11.3696i | − | 7.37135i | − | 8.81530i | − | 13.6978i | 39.7891 | 10.2551 | ||||||||||||||
12.17 | − | 0.468651i | −6.65460 | 7.78037 | − | 3.45502i | 3.11869i | 11.5900i | − | 7.39549i | 17.2837 | −1.61920 | |||||||||||||||
12.18 | − | 0.370518i | −0.548979 | 7.86272 | 11.6192i | 0.203406i | 19.9902i | − | 5.87742i | −26.6986 | 4.30511 | ||||||||||||||||
12.19 | 0.370518i | −0.548979 | 7.86272 | − | 11.6192i | − | 0.203406i | − | 19.9902i | 5.87742i | −26.6986 | 4.30511 | |||||||||||||||
12.20 | 0.468651i | −6.65460 | 7.78037 | 3.45502i | − | 3.11869i | − | 11.5900i | 7.39549i | 17.2837 | −1.61920 | ||||||||||||||||
See all 36 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 143.4.b.a | ✓ | 36 |
13.b | even | 2 | 1 | inner | 143.4.b.a | ✓ | 36 |
13.d | odd | 4 | 1 | 1859.4.a.j | 18 | ||
13.d | odd | 4 | 1 | 1859.4.a.k | 18 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
143.4.b.a | ✓ | 36 | 1.a | even | 1 | 1 | trivial |
143.4.b.a | ✓ | 36 | 13.b | even | 2 | 1 | inner |
1859.4.a.j | 18 | 13.d | odd | 4 | 1 | ||
1859.4.a.k | 18 | 13.d | odd | 4 | 1 |
Hecke kernels
This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(143, [\chi])\).