Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,5,Mod(15,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.15");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.y (of order \(12\), degree \(4\), 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: | \(9.40666664063\) |
Analytic rank: | \(0\) |
Dimension: | \(112\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
$q$-expansion
The algebraic \(q\)-expansion of this newform has not been computed, 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
15.1 | −7.48429 | − | 2.00541i | −4.04472 | − | 7.00566i | 38.1365 | + | 22.0181i | −12.4817 | + | 12.4817i | 16.2226 | + | 60.5437i | 17.8892 | − | 4.79340i | −153.607 | − | 153.607i | 7.78053 | − | 13.4763i | 118.448 | − | 68.3860i |
15.2 | −6.77988 | − | 1.81666i | 2.64324 | + | 4.57823i | 28.8102 | + | 16.6336i | 10.3095 | − | 10.3095i | −9.60378 | − | 35.8418i | 17.8892 | − | 4.79340i | −85.7005 | − | 85.7005i | 26.5265 | − | 45.9453i | −88.6258 | + | 51.1681i |
15.3 | −6.32886 | − | 1.69581i | −1.18264 | − | 2.04839i | 23.3223 | + | 13.4651i | −1.49650 | + | 1.49650i | 4.01107 | + | 14.9695i | −17.8892 | + | 4.79340i | −50.6405 | − | 50.6405i | 37.7027 | − | 65.3031i | 12.0090 | − | 6.93338i |
15.4 | −6.29214 | − | 1.68597i | 5.59104 | + | 9.68397i | 22.8922 | + | 13.2168i | 35.2136 | − | 35.2136i | −18.8527 | − | 70.3593i | −17.8892 | + | 4.79340i | −48.0589 | − | 48.0589i | −22.0196 | + | 38.1390i | −280.939 | + | 162.200i |
15.5 | −6.26332 | − | 1.67825i | −7.57425 | − | 13.1190i | 22.5562 | + | 13.0228i | 19.7636 | − | 19.7636i | 25.4230 | + | 94.8798i | −17.8892 | + | 4.79340i | −46.0601 | − | 46.0601i | −74.2384 | + | 128.585i | −156.954 | + | 90.6174i |
15.6 | −4.85396 | − | 1.30062i | −0.985675 | − | 1.70724i | 8.01295 | + | 4.62628i | −31.1904 | + | 31.1904i | 2.56397 | + | 9.56886i | −17.8892 | + | 4.79340i | 23.9760 | + | 23.9760i | 38.5569 | − | 66.7825i | 191.964 | − | 110.830i |
15.7 | −4.53284 | − | 1.21457i | −7.94599 | − | 13.7629i | 5.21509 | + | 3.01093i | −19.3441 | + | 19.3441i | 19.3019 | + | 72.0358i | 17.8892 | − | 4.79340i | 33.1102 | + | 33.1102i | −85.7774 | + | 148.571i | 111.179 | − | 64.1890i |
15.8 | −4.11478 | − | 1.10255i | 4.12647 | + | 7.14726i | 1.85941 | + | 1.07353i | −1.49291 | + | 1.49291i | −9.09931 | − | 33.9591i | 17.8892 | − | 4.79340i | 41.7282 | + | 41.7282i | 6.44444 | − | 11.1621i | 7.78901 | − | 4.49699i |
15.9 | −3.93225 | − | 1.05364i | −1.90652 | − | 3.30219i | 0.496049 | + | 0.286394i | 19.0688 | − | 19.0688i | 4.01759 | + | 14.9939i | 17.8892 | − | 4.79340i | 44.4089 | + | 44.4089i | 33.2304 | − | 57.5567i | −95.0753 | + | 54.8917i |
15.10 | −2.71417 | − | 0.727259i | 7.55128 | + | 13.0792i | −7.01860 | − | 4.05219i | −0.582134 | + | 0.582134i | −10.9835 | − | 40.9909i | −17.8892 | + | 4.79340i | 47.8932 | + | 47.8932i | −73.5436 | + | 127.381i | 2.00337 | − | 1.15665i |
15.11 | −2.09499 | − | 0.561350i | 2.63630 | + | 4.56621i | −9.78255 | − | 5.64796i | 2.05589 | − | 2.05589i | −2.95978 | − | 11.0460i | −17.8892 | + | 4.79340i | 41.8620 | + | 41.8620i | 26.5998 | − | 46.0722i | −5.46114 | + | 3.15299i |
15.12 | −1.15507 | − | 0.309500i | 2.35620 | + | 4.08106i | −12.6180 | − | 7.28501i | −29.6528 | + | 29.6528i | −1.45849 | − | 5.44317i | 17.8892 | − | 4.79340i | 25.8491 | + | 25.8491i | 29.3966 | − | 50.9164i | 43.4287 | − | 25.0735i |
15.13 | −0.544732 | − | 0.145961i | −2.95616 | − | 5.12022i | −13.5810 | − | 7.84098i | 31.2161 | − | 31.2161i | 0.862965 | + | 3.22063i | −17.8892 | + | 4.79340i | 12.6339 | + | 12.6339i | 23.0223 | − | 39.8757i | −21.5607 | + | 12.4481i |
15.14 | −0.244358 | − | 0.0654755i | −6.10406 | − | 10.5725i | −13.8010 | − | 7.96800i | −15.5864 | + | 15.5864i | 0.799333 | + | 2.98315i | −17.8892 | + | 4.79340i | 5.71279 | + | 5.71279i | −34.0191 | + | 58.9228i | 4.82917 | − | 2.78812i |
15.15 | −0.219656 | − | 0.0588566i | 5.98329 | + | 10.3634i | −13.8116 | − | 7.97414i | 26.3459 | − | 26.3459i | −0.704312 | − | 2.62853i | 17.8892 | − | 4.79340i | 5.13726 | + | 5.13726i | −31.0994 | + | 53.8658i | −7.33767 | + | 4.23640i |
15.16 | 0.455575 | + | 0.122071i | −3.69943 | − | 6.40760i | −13.6638 | − | 7.88878i | −8.56058 | + | 8.56058i | −0.903186 | − | 3.37074i | 17.8892 | − | 4.79340i | −10.5979 | − | 10.5979i | 13.1284 | − | 22.7391i | −4.94498 | + | 2.85499i |
15.17 | 1.92597 | + | 0.516062i | 7.99140 | + | 13.8415i | −10.4134 | − | 6.01216i | −14.2080 | + | 14.2080i | 8.24812 | + | 30.7824i | 17.8892 | − | 4.79340i | −39.5117 | − | 39.5117i | −87.2249 | + | 151.078i | −34.6965 | + | 20.0320i |
15.18 | 1.99770 | + | 0.535283i | −8.78280 | − | 15.2123i | −10.1521 | − | 5.86133i | 26.5980 | − | 26.5980i | −9.40257 | − | 35.0909i | 17.8892 | − | 4.79340i | −40.5422 | − | 40.5422i | −113.775 | + | 197.065i | 67.3723 | − | 38.8974i |
15.19 | 2.22041 | + | 0.594958i | 1.11959 | + | 1.93919i | −9.28015 | − | 5.35790i | −5.87167 | + | 5.87167i | 1.33222 | + | 4.97191i | −17.8892 | + | 4.79340i | −43.4253 | − | 43.4253i | 37.9930 | − | 65.8059i | −16.5309 | + | 9.54413i |
15.20 | 3.65151 | + | 0.978420i | 4.24787 | + | 7.35753i | −1.48017 | − | 0.854576i | −27.1569 | + | 27.1569i | 8.31241 | + | 31.0223i | −17.8892 | + | 4.79340i | −47.3382 | − | 47.3382i | 4.41112 | − | 7.64028i | −125.735 | + | 72.5929i |
See next 80 embeddings (of 112 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
13.f | odd | 12 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 91.5.y.a | ✓ | 112 |
13.f | odd | 12 | 1 | inner | 91.5.y.a | ✓ | 112 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
91.5.y.a | ✓ | 112 | 1.a | even | 1 | 1 | trivial |
91.5.y.a | ✓ | 112 | 13.f | odd | 12 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(91, [\chi])\).