Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,3,Mod(34,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.34");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.f (of order \(4\), 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: | \(3.89646778035\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
34.1 | −2.64015 | − | 2.64015i | −4.33590 | 9.94077i | 1.25926 | + | 1.25926i | 11.4474 | + | 11.4474i | −0.913684 | + | 0.913684i | 15.6845 | − | 15.6845i | 9.80004 | − | 6.64925i | |||||||
34.2 | −2.22621 | − | 2.22621i | −0.558224 | 5.91203i | −6.02578 | − | 6.02578i | 1.24272 | + | 1.24272i | 9.68125 | − | 9.68125i | 4.25659 | − | 4.25659i | −8.68839 | 26.8293i | ||||||||
34.3 | −1.85438 | − | 1.85438i | 5.20150 | 2.87745i | 2.96117 | + | 2.96117i | −9.64555 | − | 9.64555i | 2.87608 | − | 2.87608i | −2.08163 | + | 2.08163i | 18.0556 | − | 10.9823i | |||||||
34.4 | −1.73011 | − | 1.73011i | 0.410741 | 1.98654i | 4.09492 | + | 4.09492i | −0.710625 | − | 0.710625i | −5.63695 | + | 5.63695i | −3.48350 | + | 3.48350i | −8.83129 | − | 14.1693i | |||||||
34.5 | −1.68515 | − | 1.68515i | 3.72208 | 1.67948i | −6.45193 | − | 6.45193i | −6.27228 | − | 6.27228i | −5.94039 | + | 5.94039i | −3.91043 | + | 3.91043i | 4.85388 | 21.7450i | ||||||||
34.6 | −1.59151 | − | 1.59151i | −2.93230 | 1.06581i | −1.63050 | − | 1.63050i | 4.66679 | + | 4.66679i | −2.09617 | + | 2.09617i | −4.66980 | + | 4.66980i | −0.401600 | 5.18992i | ||||||||
34.7 | −1.51765 | − | 1.51765i | −4.16131 | 0.606507i | 5.29838 | + | 5.29838i | 6.31540 | + | 6.31540i | 6.10478 | − | 6.10478i | −5.15013 | + | 5.15013i | 8.31650 | − | 16.0822i | |||||||
34.8 | −0.776817 | − | 0.776817i | 3.30077 | − | 2.79311i | −0.0738022 | − | 0.0738022i | −2.56409 | − | 2.56409i | 6.38010 | − | 6.38010i | −5.27701 | + | 5.27701i | 1.89508 | 0.114662i | |||||||
34.9 | −0.559583 | − | 0.559583i | −0.674236 | − | 3.37373i | −0.687945 | − | 0.687945i | 0.377291 | + | 0.377291i | 2.77474 | − | 2.77474i | −4.12622 | + | 4.12622i | −8.54541 | 0.769925i | |||||||
34.10 | −0.552131 | − | 0.552131i | −5.92566 | − | 3.39030i | −4.73402 | − | 4.73402i | 3.27174 | + | 3.27174i | −0.106091 | + | 0.106091i | −4.08041 | + | 4.08041i | 26.1135 | 5.22760i | |||||||
34.11 | −0.0486638 | − | 0.0486638i | −0.462719 | − | 3.99526i | −2.85396 | − | 2.85396i | 0.0225177 | + | 0.0225177i | −7.80024 | + | 7.80024i | −0.389080 | + | 0.389080i | −8.78589 | 0.277769i | |||||||
34.12 | 0.155288 | + | 0.155288i | 1.56388 | − | 3.95177i | 6.66238 | + | 6.66238i | 0.242851 | + | 0.242851i | 0.683897 | − | 0.683897i | 1.23481 | − | 1.23481i | −6.55429 | 2.06918i | |||||||
34.13 | 0.356298 | + | 0.356298i | 5.60622 | − | 3.74610i | 1.97185 | + | 1.97185i | 1.99748 | + | 1.99748i | −7.27233 | + | 7.27233i | 2.75992 | − | 2.75992i | 22.4297 | 1.40513i | |||||||
34.14 | 0.691450 | + | 0.691450i | 3.83291 | − | 3.04379i | −4.28548 | − | 4.28548i | 2.65027 | + | 2.65027i | 1.74284 | − | 1.74284i | 4.87043 | − | 4.87043i | 5.69120 | − | 5.92639i | ||||||
34.15 | 1.26289 | + | 1.26289i | −1.31481 | − | 0.810231i | −4.90134 | − | 4.90134i | −1.66046 | − | 1.66046i | 3.17698 | − | 3.17698i | 6.07478 | − | 6.07478i | −7.27126 | − | 12.3797i | ||||||
34.16 | 1.32847 | + | 1.32847i | −4.01579 | − | 0.470326i | 0.202377 | + | 0.202377i | −5.33487 | − | 5.33487i | 7.08212 | − | 7.08212i | 5.93870 | − | 5.93870i | 7.12659 | 0.537703i | |||||||
34.17 | 1.53765 | + | 1.53765i | 1.81506 | 0.728748i | 3.39071 | + | 3.39071i | 2.79093 | + | 2.79093i | 4.13599 | − | 4.13599i | 5.03005 | − | 5.03005i | −5.70557 | 10.4275i | ||||||||
34.18 | 2.04521 | + | 2.04521i | 2.72146 | 4.36577i | 0.836799 | + | 0.836799i | 5.56597 | + | 5.56597i | −4.60563 | + | 4.60563i | −0.748085 | + | 0.748085i | −1.59364 | 3.42286i | ||||||||
34.19 | 2.20615 | + | 2.20615i | −2.86898 | 5.73423i | 3.26224 | + | 3.26224i | −6.32941 | − | 6.32941i | −5.19398 | + | 5.19398i | −3.82598 | + | 3.82598i | −0.768954 | 14.3940i | ||||||||
34.20 | 2.34575 | + | 2.34575i | −3.89202 | 7.00508i | −6.20731 | − | 6.20731i | −9.12970 | − | 9.12970i | −4.51214 | + | 4.51214i | −7.04916 | + | 7.04916i | 6.14781 | − | 29.1216i | |||||||
See all 44 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.d | odd | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 143.3.f.a | ✓ | 44 |
13.d | odd | 4 | 1 | inner | 143.3.f.a | ✓ | 44 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
143.3.f.a | ✓ | 44 | 1.a | even | 1 | 1 | trivial |
143.3.f.a | ✓ | 44 | 13.d | odd | 4 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(143, [\chi])\).