Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,5,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, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
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: | \(2.37750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(70\) |
Relative dimension: | \(7\) 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 | −6.23539 | − | 1.83088i | 6.55829 | − | 7.56867i | 22.0680 | + | 14.1822i | −37.2451 | − | 5.35504i | −54.7508 | + | 35.1862i | −43.4159 | + | 19.8274i | −43.5454 | − | 50.2541i | −2.74610 | − | 19.0996i | 222.434 | + | 101.582i |
5.2 | −5.33512 | − | 1.56653i | −2.92721 | + | 3.37818i | 12.5494 | + | 8.06502i | 31.6604 | + | 4.55208i | 20.9090 | − | 13.4374i | 36.8795 | − | 16.8423i | 3.94161 | + | 4.54886i | 8.68396 | + | 60.3983i | −161.781 | − | 73.8829i |
5.3 | −0.880608 | − | 0.258570i | −5.57964 | + | 6.43925i | −12.7514 | − | 8.19486i | −17.0417 | − | 2.45023i | 6.57847 | − | 4.22773i | −31.0622 | + | 14.1856i | 18.7264 | + | 21.6114i | 1.19597 | + | 8.31815i | 14.3735 | + | 6.56417i |
5.4 | −0.152216 | − | 0.0446948i | 7.85234 | − | 9.06208i | −13.4389 | − | 8.63665i | 0.171500 | + | 0.0246579i | −1.60028 | + | 1.02844i | 52.7309 | − | 24.0814i | 3.32183 | + | 3.83359i | −8.93460 | − | 62.1415i | −0.0250030 | − | 0.0114185i |
5.5 | 4.08377 | + | 1.19910i | 2.59819 | − | 2.99847i | 1.77931 | + | 1.14349i | 35.9653 | + | 5.17103i | 14.2059 | − | 9.12957i | −63.1747 | + | 28.8509i | −38.7002 | − | 44.6624i | 9.28727 | + | 64.5944i | 140.674 | + | 64.2434i |
5.6 | 5.24881 | + | 1.54119i | −10.2768 | + | 11.8601i | 11.7147 | + | 7.52859i | 13.8853 | + | 1.99640i | −72.2198 | + | 46.4128i | 72.8498 | − | 33.2694i | −7.43228 | − | 8.57731i | −23.5210 | − | 163.592i | 69.8043 | + | 31.8786i |
5.7 | 6.27256 | + | 1.84179i | 3.63756 | − | 4.19797i | 22.4927 | + | 14.4552i | −41.1469 | − | 5.91603i | 30.5486 | − | 19.6324i | 0.548908 | − | 0.250678i | 45.9665 | + | 53.0482i | 7.13641 | + | 49.6348i | −247.200 | − | 112.893i |
7.1 | −4.13729 | + | 4.77469i | −5.59893 | + | 3.59821i | −3.40343 | − | 23.6714i | 0.838951 | − | 0.383136i | 5.98405 | − | 41.6200i | −15.6319 | − | 53.2373i | 42.0661 | + | 27.0342i | −15.2477 | + | 33.3879i | −1.64163 | + | 5.59087i |
7.2 | −3.88218 | + | 4.48028i | 14.3217 | − | 9.20399i | −2.72451 | − | 18.9494i | 14.9307 | − | 6.81860i | −14.3630 | + | 99.8968i | 18.1967 | + | 61.9723i | 15.6809 | + | 10.0775i | 86.7488 | − | 189.953i | −27.4143 | + | 93.3646i |
7.3 | −1.65795 | + | 1.91338i | −0.476447 | + | 0.306194i | 1.36482 | + | 9.49254i | −24.0936 | + | 11.0032i | 0.204062 | − | 1.41928i | 12.1157 | + | 41.2622i | −54.5034 | − | 35.0272i | −33.5154 | + | 73.3884i | 18.8928 | − | 64.3430i |
7.4 | 0.246852 | − | 0.284882i | 2.49375 | − | 1.60264i | 2.25682 | + | 15.6965i | 37.9584 | − | 17.3350i | 0.159024 | − | 1.10604i | −7.04577 | − | 23.9957i | 10.1026 | + | 6.49253i | −29.9983 | + | 65.6870i | 4.43167 | − | 15.0929i |
7.5 | 1.24584 | − | 1.43777i | −13.2108 | + | 8.49010i | 1.76196 | + | 12.2547i | −8.32630 | + | 3.80249i | −4.25173 | + | 29.5714i | −1.18231 | − | 4.02657i | 45.4215 | + | 29.1907i | 68.7961 | − | 150.642i | −4.90608 | + | 16.7086i |
7.6 | 2.42804 | − | 2.80211i | 10.9682 | − | 7.04881i | 0.320606 | + | 2.22986i | −27.0695 | + | 12.3622i | 6.87962 | − | 47.8488i | −5.49864 | − | 18.7267i | 56.9329 | + | 36.5886i | 36.9662 | − | 80.9446i | −31.0856 | + | 105.868i |
7.7 | 4.33983 | − | 5.00844i | −1.84102 | + | 1.18315i | −3.97323 | − | 27.6344i | 8.83387 | − | 4.03429i | −2.06398 | + | 14.3553i | 6.57566 | + | 22.3946i | −66.4470 | − | 42.7029i | −31.6591 | + | 69.3238i | 18.1320 | − | 61.7520i |
10.1 | −4.13729 | − | 4.77469i | −5.59893 | − | 3.59821i | −3.40343 | + | 23.6714i | 0.838951 | + | 0.383136i | 5.98405 | + | 41.6200i | −15.6319 | + | 53.2373i | 42.0661 | − | 27.0342i | −15.2477 | − | 33.3879i | −1.64163 | − | 5.59087i |
10.2 | −3.88218 | − | 4.48028i | 14.3217 | + | 9.20399i | −2.72451 | + | 18.9494i | 14.9307 | + | 6.81860i | −14.3630 | − | 99.8968i | 18.1967 | − | 61.9723i | 15.6809 | − | 10.0775i | 86.7488 | + | 189.953i | −27.4143 | − | 93.3646i |
10.3 | −1.65795 | − | 1.91338i | −0.476447 | − | 0.306194i | 1.36482 | − | 9.49254i | −24.0936 | − | 11.0032i | 0.204062 | + | 1.41928i | 12.1157 | − | 41.2622i | −54.5034 | + | 35.0272i | −33.5154 | − | 73.3884i | 18.8928 | + | 64.3430i |
10.4 | 0.246852 | + | 0.284882i | 2.49375 | + | 1.60264i | 2.25682 | − | 15.6965i | 37.9584 | + | 17.3350i | 0.159024 | + | 1.10604i | −7.04577 | + | 23.9957i | 10.1026 | − | 6.49253i | −29.9983 | − | 65.6870i | 4.43167 | + | 15.0929i |
10.5 | 1.24584 | + | 1.43777i | −13.2108 | − | 8.49010i | 1.76196 | − | 12.2547i | −8.32630 | − | 3.80249i | −4.25173 | − | 29.5714i | −1.18231 | + | 4.02657i | 45.4215 | − | 29.1907i | 68.7961 | + | 150.642i | −4.90608 | − | 16.7086i |
10.6 | 2.42804 | + | 2.80211i | 10.9682 | + | 7.04881i | 0.320606 | − | 2.22986i | −27.0695 | − | 12.3622i | 6.87962 | + | 47.8488i | −5.49864 | + | 18.7267i | 56.9329 | − | 36.5886i | 36.9662 | + | 80.9446i | −31.0856 | − | 105.868i |
See all 70 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 | 23.5.d.a | ✓ | 70 |
23.d | odd | 22 | 1 | inner | 23.5.d.a | ✓ | 70 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
23.5.d.a | ✓ | 70 | 1.a | even | 1 | 1 | trivial |
23.5.d.a | ✓ | 70 | 23.d | odd | 22 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(23, [\chi])\).