Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [92,7,Mod(5,92)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(92, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("92.5");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 92 = 2^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 92.f (of order \(22\), degree \(10\), 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: | \(21.1649756930\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{22})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{22}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5.1 | 0 | −31.8406 | + | 36.7461i | 0 | 211.302 | + | 30.3806i | 0 | 155.741 | − | 71.1244i | 0 | −232.699 | − | 1618.46i | 0 | ||||||||||
5.2 | 0 | −31.4750 | + | 36.3241i | 0 | −86.8435 | − | 12.4862i | 0 | −521.394 | + | 238.113i | 0 | −225.016 | − | 1565.02i | 0 | ||||||||||
5.3 | 0 | −21.7022 | + | 25.0456i | 0 | −134.521 | − | 19.3413i | 0 | 533.764 | − | 243.762i | 0 | −52.5522 | − | 365.509i | 0 | ||||||||||
5.4 | 0 | −18.2424 | + | 21.0528i | 0 | −10.3368 | − | 1.48621i | 0 | 152.054 | − | 69.4408i | 0 | −6.68949 | − | 46.5264i | 0 | ||||||||||
5.5 | 0 | −10.6880 | + | 12.3347i | 0 | 98.7910 | + | 14.2040i | 0 | −288.749 | + | 131.867i | 0 | 65.8380 | + | 457.913i | 0 | ||||||||||
5.6 | 0 | −4.44687 | + | 5.13196i | 0 | −170.627 | − | 24.5325i | 0 | −231.772 | + | 105.847i | 0 | 97.1852 | + | 675.938i | 0 | ||||||||||
5.7 | 0 | 4.84460 | − | 5.59096i | 0 | 143.748 | + | 20.6679i | 0 | 484.055 | − | 221.060i | 0 | 95.9588 | + | 667.408i | 0 | ||||||||||
5.8 | 0 | 8.00746 | − | 9.24110i | 0 | 136.076 | + | 19.5648i | 0 | −144.161 | + | 65.8360i | 0 | 82.4690 | + | 573.584i | 0 | ||||||||||
5.9 | 0 | 14.9815 | − | 17.2895i | 0 | −102.429 | − | 14.7271i | 0 | 247.858 | − | 113.193i | 0 | 29.2639 | + | 203.535i | 0 | ||||||||||
5.10 | 0 | 21.5982 | − | 24.9257i | 0 | −140.338 | − | 20.1776i | 0 | −156.734 | + | 71.5779i | 0 | −51.0587 | − | 355.121i | 0 | ||||||||||
5.11 | 0 | 29.9956 | − | 34.6167i | 0 | 61.0797 | + | 8.78194i | 0 | 428.582 | − | 195.727i | 0 | −194.836 | − | 1355.12i | 0 | ||||||||||
5.12 | 0 | 30.2625 | − | 34.9248i | 0 | 118.038 | + | 16.9713i | 0 | −529.590 | + | 241.856i | 0 | −200.175 | − | 1392.24i | 0 | ||||||||||
17.1 | 0 | −48.3297 | − | 14.1909i | 0 | −38.1811 | − | 59.4110i | 0 | 304.114 | + | 43.7250i | 0 | 1521.10 | + | 977.552i | 0 | ||||||||||
17.2 | 0 | −36.0323 | − | 10.5800i | 0 | 28.1134 | + | 43.7453i | 0 | −329.258 | − | 47.3401i | 0 | 573.113 | + | 368.318i | 0 | ||||||||||
17.3 | 0 | −24.4673 | − | 7.18426i | 0 | 112.776 | + | 175.483i | 0 | 69.0501 | + | 9.92790i | 0 | −66.2372 | − | 42.5681i | 0 | ||||||||||
17.4 | 0 | −21.1457 | − | 6.20893i | 0 | −123.835 | − | 192.691i | 0 | −636.281 | − | 91.4834i | 0 | −204.686 | − | 131.543i | 0 | ||||||||||
17.5 | 0 | −16.2735 | − | 4.77832i | 0 | −62.3371 | − | 96.9984i | 0 | 166.217 | + | 23.8983i | 0 | −371.281 | − | 238.608i | 0 | ||||||||||
17.6 | 0 | −7.90769 | − | 2.32191i | 0 | −15.3909 | − | 23.9488i | 0 | 510.630 | + | 73.4175i | 0 | −556.134 | − | 357.405i | 0 | ||||||||||
17.7 | 0 | 5.34629 | + | 1.56981i | 0 | 31.8228 | + | 49.5172i | 0 | −219.578 | − | 31.5705i | 0 | −587.155 | − | 377.342i | 0 | ||||||||||
17.8 | 0 | 16.1437 | + | 4.74023i | 0 | −62.8173 | − | 97.7456i | 0 | 48.1080 | + | 6.91689i | 0 | −375.123 | − | 241.077i | 0 | ||||||||||
See next 80 embeddings (of 120 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
23.d | odd | 22 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 92.7.f.a | ✓ | 120 |
23.d | odd | 22 | 1 | inner | 92.7.f.a | ✓ | 120 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
92.7.f.a | ✓ | 120 | 1.a | even | 1 | 1 | trivial |
92.7.f.a | ✓ | 120 | 23.d | odd | 22 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(92, [\chi])\).