Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,3,Mod(5,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.d (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: | \(0.626704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(3\) 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 | −3.10125 | − | 0.910608i | −3.16934 | + | 3.65762i | 5.42352 | + | 3.48548i | −5.40865 | − | 0.777647i | 13.1596 | − | 8.45714i | −0.889564 | + | 0.406250i | −5.17926 | − | 5.97719i | −2.05259 | − | 14.2761i | 16.0654 | + | 7.33684i |
5.2 | −1.80062 | − | 0.528710i | 2.35762 | − | 2.72084i | −0.402313 | − | 0.258551i | 5.05070 | + | 0.726181i | −5.68372 | + | 3.65270i | −8.85488 | + | 4.04389i | 5.50346 | + | 6.35133i | −0.563759 | − | 3.92103i | −8.71046 | − | 3.97793i |
5.3 | 1.44626 | + | 0.424661i | −0.590042 | + | 0.680945i | −1.45368 | − | 0.934223i | −1.77862 | − | 0.255727i | −1.14252 | + | 0.734256i | 2.68734 | − | 1.22727i | −5.65401 | − | 6.52507i | 1.16530 | + | 8.10482i | −2.46375 | − | 1.12516i |
7.1 | −1.38322 | + | 1.59632i | −3.80315 | + | 2.44414i | −0.0656849 | − | 0.456848i | 6.26010 | − | 2.85889i | 1.35897 | − | 9.45184i | 2.54176 | + | 8.65643i | −6.28757 | − | 4.04078i | 4.75142 | − | 10.4042i | −4.09539 | + | 13.9476i |
7.2 | −0.881085 | + | 1.01683i | 2.64748 | − | 1.70143i | 0.311634 | + | 2.16747i | −2.08252 | + | 0.951056i | −0.602595 | + | 4.19114i | −2.90589 | − | 9.89656i | −7.00598 | − | 4.50247i | 0.375553 | − | 0.822346i | 0.867820 | − | 2.95552i |
7.3 | 1.59301 | − | 1.83844i | −1.87410 | + | 1.20441i | −0.272894 | − | 1.89802i | −2.69128 | + | 1.22907i | −0.771235 | + | 5.36406i | −1.33225 | − | 4.53722i | 4.26162 | + | 2.73877i | −1.67709 | + | 3.67232i | −2.02769 | + | 6.90566i |
10.1 | −1.38322 | − | 1.59632i | −3.80315 | − | 2.44414i | −0.0656849 | + | 0.456848i | 6.26010 | + | 2.85889i | 1.35897 | + | 9.45184i | 2.54176 | − | 8.65643i | −6.28757 | + | 4.04078i | 4.75142 | + | 10.4042i | −4.09539 | − | 13.9476i |
10.2 | −0.881085 | − | 1.01683i | 2.64748 | + | 1.70143i | 0.311634 | − | 2.16747i | −2.08252 | − | 0.951056i | −0.602595 | − | 4.19114i | −2.90589 | + | 9.89656i | −7.00598 | + | 4.50247i | 0.375553 | + | 0.822346i | 0.867820 | + | 2.95552i |
10.3 | 1.59301 | + | 1.83844i | −1.87410 | − | 1.20441i | −0.272894 | + | 1.89802i | −2.69128 | − | 1.22907i | −0.771235 | − | 5.36406i | −1.33225 | + | 4.53722i | 4.26162 | − | 2.73877i | −1.67709 | − | 3.67232i | −2.02769 | − | 6.90566i |
11.1 | −1.94274 | + | 1.24852i | −0.365090 | + | 2.53926i | 0.553766 | − | 1.21258i | 0.682875 | + | 2.32566i | −2.46105 | − | 5.38894i | 6.72814 | − | 5.82996i | −0.876504 | − | 6.09622i | 2.32089 | + | 0.681474i | −4.23029 | − | 3.66556i |
11.2 | 0.0163142 | − | 0.0104845i | 0.749667 | − | 5.21405i | −1.66150 | + | 3.63819i | 1.45779 | + | 4.96477i | −0.0424364 | − | 0.0929228i | −1.27914 | + | 1.10838i | 0.0220779 | + | 0.153555i | −17.9889 | − | 5.28201i | 0.0758357 | + | 0.0657120i |
11.3 | 1.20995 | − | 0.777587i | −0.238691 | + | 1.66013i | −0.802326 | + | 1.75685i | −2.65558 | − | 9.04406i | 1.00209 | + | 2.19428i | −5.31379 | + | 4.60443i | 1.21408 | + | 8.44409i | 5.93637 | + | 1.74307i | −10.2457 | − | 8.87791i |
14.1 | −3.10125 | + | 0.910608i | −3.16934 | − | 3.65762i | 5.42352 | − | 3.48548i | −5.40865 | + | 0.777647i | 13.1596 | + | 8.45714i | −0.889564 | − | 0.406250i | −5.17926 | + | 5.97719i | −2.05259 | + | 14.2761i | 16.0654 | − | 7.33684i |
14.2 | −1.80062 | + | 0.528710i | 2.35762 | + | 2.72084i | −0.402313 | + | 0.258551i | 5.05070 | − | 0.726181i | −5.68372 | − | 3.65270i | −8.85488 | − | 4.04389i | 5.50346 | − | 6.35133i | −0.563759 | + | 3.92103i | −8.71046 | + | 3.97793i |
14.3 | 1.44626 | − | 0.424661i | −0.590042 | − | 0.680945i | −1.45368 | + | 0.934223i | −1.77862 | + | 0.255727i | −1.14252 | − | 0.734256i | 2.68734 | + | 1.22727i | −5.65401 | + | 6.52507i | 1.16530 | − | 8.10482i | −2.46375 | + | 1.12516i |
15.1 | −0.387684 | + | 2.69640i | −0.141551 | − | 0.309954i | −3.28232 | − | 0.963778i | −0.353921 | + | 0.306674i | 0.890639 | − | 0.261515i | 4.93105 | − | 7.67286i | −0.655341 | + | 1.43500i | 5.81771 | − | 6.71400i | −0.689708 | − | 1.07321i |
15.2 | 0.123822 | − | 0.861198i | −1.04228 | − | 2.28229i | 3.11164 | + | 0.913660i | −1.80972 | + | 1.56813i | −2.09456 | + | 0.615017i | −6.61670 | + | 10.2958i | 2.61786 | − | 5.73232i | 1.77128 | − | 2.04416i | 1.12639 | + | 1.75270i |
15.3 | 0.496456 | − | 3.45293i | 1.53764 | + | 3.36695i | −7.83827 | − | 2.30152i | −4.84192 | + | 4.19555i | 12.3892 | − | 3.63780i | 3.55260 | − | 5.52795i | −6.04175 | + | 13.2296i | −3.07830 | + | 3.55255i | 12.0831 | + | 18.8017i |
17.1 | −1.55977 | + | 3.41542i | 0.201951 | + | 0.0592983i | −6.61275 | − | 7.63152i | 2.90325 | + | 4.51755i | −0.517526 | + | 0.597257i | 7.13192 | + | 1.02541i | 21.9686 | − | 6.45058i | −7.53401 | − | 4.84182i | −19.9577 | + | 2.86949i |
17.2 | −0.282292 | + | 0.618133i | 0.844537 | + | 0.247978i | 2.31704 | + | 2.67401i | −3.24760 | − | 5.05336i | −0.391690 | + | 0.452034i | −3.20136 | − | 0.460286i | −4.91504 | + | 1.44319i | −6.91953 | − | 4.44691i | 4.04042 | − | 0.580925i |
See all 30 embeddings |
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 | 23.3.d.a | ✓ | 30 |
3.b | odd | 2 | 1 | 207.3.j.a | 30 | ||
4.b | odd | 2 | 1 | 368.3.p.a | 30 | ||
23.c | even | 11 | 1 | 529.3.b.b | 30 | ||
23.d | odd | 22 | 1 | inner | 23.3.d.a | ✓ | 30 |
23.d | odd | 22 | 1 | 529.3.b.b | 30 | ||
69.g | even | 22 | 1 | 207.3.j.a | 30 | ||
92.h | even | 22 | 1 | 368.3.p.a | 30 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
23.3.d.a | ✓ | 30 | 1.a | even | 1 | 1 | trivial |
23.3.d.a | ✓ | 30 | 23.d | odd | 22 | 1 | inner |
207.3.j.a | 30 | 3.b | odd | 2 | 1 | ||
207.3.j.a | 30 | 69.g | even | 22 | 1 | ||
368.3.p.a | 30 | 4.b | odd | 2 | 1 | ||
368.3.p.a | 30 | 92.h | even | 22 | 1 | ||
529.3.b.b | 30 | 23.c | even | 11 | 1 | ||
529.3.b.b | 30 | 23.d | odd | 22 | 1 |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(23, [\chi])\).