Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (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: | \(4.44490841261\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7.1 | − | 7.38404i | 15.2777 | − | 8.82059i | −38.5241 | −17.1186 | + | 9.88344i | −65.1316 | − | 112.811i | 36.3076 | + | 20.9622i | 166.319i | 115.106 | − | 199.369i | 72.9798 | + | 126.405i | |||||
7.2 | − | 7.27000i | −9.67914 | + | 5.58826i | −36.8529 | 5.33236 | − | 3.07864i | 40.6266 | + | 70.3674i | 35.8849 | + | 20.7182i | 151.601i | 21.9572 | − | 38.0310i | −22.3817 | − | 38.7662i | |||||
7.3 | − | 5.51064i | −1.33569 | + | 0.771161i | −14.3672 | −29.9636 | + | 17.2995i | 4.24959 | + | 7.36051i | −50.7143 | − | 29.2799i | − | 8.99803i | −39.3106 | + | 68.0880i | 95.3312 | + | 165.119i | ||||
7.4 | − | 5.28884i | 3.72701 | − | 2.15179i | −11.9718 | 30.9460 | − | 17.8667i | −11.3805 | − | 19.7116i | −25.0066 | − | 14.4376i | − | 21.3046i | −31.2396 | + | 54.1085i | −94.4939 | − | 163.668i | ||||
7.5 | − | 2.95871i | 6.98373 | − | 4.03206i | 7.24603 | 4.46909 | − | 2.58023i | −11.9297 | − | 20.6628i | 37.3312 | + | 21.5532i | − | 68.7783i | −7.98499 | + | 13.8304i | −7.63415 | − | 13.2227i | ||||
7.6 | − | 2.55236i | −13.8661 | + | 8.00559i | 9.48548 | 27.9587 | − | 16.1420i | 20.4331 | + | 35.3912i | −55.0431 | − | 31.7792i | − | 65.0480i | 87.6790 | − | 151.865i | −41.2001 | − | 71.3606i | ||||
7.7 | − | 2.45393i | −7.53154 | + | 4.34833i | 9.97824 | −12.0383 | + | 6.95034i | 10.6705 | + | 18.4818i | 83.6059 | + | 48.2699i | − | 63.7487i | −2.68397 | + | 4.64877i | 17.0556 | + | 29.5412i | ||||
7.8 | 0.411879i | 10.8202 | − | 6.24704i | 15.8304 | −3.72754 | + | 2.15210i | 2.57302 | + | 4.45661i | −34.4055 | − | 19.8640i | 13.1103i | 37.5509 | − | 65.0401i | −0.886404 | − | 1.53530i | ||||||
7.9 | 1.02950i | −6.61850 | + | 3.82119i | 14.9401 | −23.6208 | + | 13.6375i | −3.93391 | − | 6.81373i | −37.2107 | − | 21.4836i | 31.8528i | −11.2970 | + | 19.5669i | −14.0398 | − | 24.3176i | ||||||
7.10 | 2.98081i | −1.27161 | + | 0.734162i | 7.11478 | 26.8620 | − | 15.5088i | −2.18840 | − | 3.79041i | 15.5504 | + | 8.97804i | 68.9007i | −39.4220 | + | 68.2809i | 46.2288 | + | 80.0706i | ||||||
7.11 | 4.83828i | 7.61693 | − | 4.39763i | −7.40895 | −37.8372 | + | 21.8453i | 21.2770 | + | 36.8528i | 66.6485 | + | 38.4795i | 41.5659i | −1.82162 | + | 3.15513i | −105.694 | − | 183.067i | ||||||
7.12 | 5.69416i | −13.9948 | + | 8.07993i | −16.4234 | 2.48060 | − | 1.43217i | −46.0084 | − | 79.6889i | 31.0431 | + | 17.9227i | − | 2.41117i | 90.0705 | − | 156.007i | 8.15502 | + | 14.1249i | |||||
7.13 | 6.51108i | 13.8942 | − | 8.02184i | −26.3942 | 31.7247 | − | 18.3162i | 52.2308 | + | 90.4665i | 5.86707 | + | 3.38735i | − | 67.6775i | 88.1998 | − | 152.766i | 119.259 | + | 206.562i | |||||
7.14 | 6.75666i | −1.02237 | + | 0.590266i | −29.6524 | −6.96733 | + | 4.02259i | −3.98823 | − | 6.90781i | −45.3584 | − | 26.1877i | − | 92.2449i | −39.8032 | + | 68.9411i | −27.1793 | − | 47.0759i | |||||
37.1 | − | 6.75666i | −1.02237 | − | 0.590266i | −29.6524 | −6.96733 | − | 4.02259i | −3.98823 | + | 6.90781i | −45.3584 | + | 26.1877i | 92.2449i | −39.8032 | − | 68.9411i | −27.1793 | + | 47.0759i | |||||
37.2 | − | 6.51108i | 13.8942 | + | 8.02184i | −26.3942 | 31.7247 | + | 18.3162i | 52.2308 | − | 90.4665i | 5.86707 | − | 3.38735i | 67.6775i | 88.1998 | + | 152.766i | 119.259 | − | 206.562i | |||||
37.3 | − | 5.69416i | −13.9948 | − | 8.07993i | −16.4234 | 2.48060 | + | 1.43217i | −46.0084 | + | 79.6889i | 31.0431 | − | 17.9227i | 2.41117i | 90.0705 | + | 156.007i | 8.15502 | − | 14.1249i | |||||
37.4 | − | 4.83828i | 7.61693 | + | 4.39763i | −7.40895 | −37.8372 | − | 21.8453i | 21.2770 | − | 36.8528i | 66.6485 | − | 38.4795i | − | 41.5659i | −1.82162 | − | 3.15513i | −105.694 | + | 183.067i | ||||
37.5 | − | 2.98081i | −1.27161 | − | 0.734162i | 7.11478 | 26.8620 | + | 15.5088i | −2.18840 | + | 3.79041i | 15.5504 | − | 8.97804i | − | 68.9007i | −39.4220 | − | 68.2809i | 46.2288 | − | 80.0706i | ||||
37.6 | − | 1.02950i | −6.61850 | − | 3.82119i | 14.9401 | −23.6208 | − | 13.6375i | −3.93391 | + | 6.81373i | −37.2107 | + | 21.4836i | − | 31.8528i | −11.2970 | − | 19.5669i | −14.0398 | + | 24.3176i | ||||
See all 28 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
43.d | odd | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 43.5.d.a | ✓ | 28 |
43.d | odd | 6 | 1 | inner | 43.5.d.a | ✓ | 28 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
43.5.d.a | ✓ | 28 | 1.a | even | 1 | 1 | trivial |
43.5.d.a | ✓ | 28 | 43.d | odd | 6 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(43, [\chi])\).