Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,4,Mod(5,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 16]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.t (of order \(18\), degree \(6\), 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: | \(8.96829032087\) |
Analytic rank: | \(0\) |
Dimension: | \(348\) |
Relative dimension: | \(58\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
$q$-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 | −2.82713 | + | 0.0857083i | −6.31470 | − | 1.11345i | 7.98531 | − | 0.484617i | 13.6906 | − | 16.3158i | 17.9479 | + | 2.60665i | 2.50109 | + | 4.33202i | −22.5340 | + | 2.05448i | 13.2639 | + | 4.82767i | −37.3066 | + | 47.3002i |
5.2 | −2.81612 | − | 0.263534i | −0.304087 | − | 0.0536187i | 7.86110 | + | 1.48429i | −12.5870 | + | 15.0006i | 0.842215 | + | 0.231134i | −3.26800 | − | 5.66034i | −21.7467 | − | 6.25161i | −25.2821 | − | 9.20193i | 39.3997 | − | 38.9264i |
5.3 | −2.81245 | + | 0.300165i | 4.63211 | + | 0.816766i | 7.81980 | − | 1.68840i | 0.297222 | − | 0.354215i | −13.2728 | − | 0.906719i | −12.9666 | − | 22.4588i | −21.4860 | + | 7.09579i | −4.58236 | − | 1.66784i | −0.729600 | + | 1.08543i |
5.4 | −2.80737 | − | 0.344520i | −6.82434 | − | 1.20332i | 7.76261 | + | 1.93439i | −1.31007 | + | 1.56128i | 18.7439 | + | 5.72927i | −8.09624 | − | 14.0231i | −21.1261 | − | 8.10492i | 19.7520 | + | 7.18914i | 4.21573 | − | 3.93174i |
5.5 | −2.79657 | + | 0.423345i | 2.55460 | + | 0.450445i | 7.64156 | − | 2.36782i | −0.869689 | + | 1.03646i | −7.33480 | − | 0.178223i | 9.58545 | + | 16.6025i | −20.3677 | + | 9.85678i | −19.0486 | − | 6.93313i | 1.99337 | − | 3.26669i |
5.6 | −2.73220 | + | 0.731475i | 9.54931 | + | 1.68380i | 6.92989 | − | 3.99708i | 8.11803 | − | 9.67470i | −27.3223 | + | 2.38460i | 10.6991 | + | 18.5314i | −16.0101 | + | 15.9899i | 62.9825 | + | 22.9237i | −15.1033 | + | 32.3714i |
5.7 | −2.56317 | + | 1.19588i | −9.54931 | − | 1.68380i | 5.13972 | − | 6.13052i | −8.11803 | + | 9.67470i | 26.4902 | − | 7.10400i | 10.6991 | + | 18.5314i | −5.84259 | + | 21.8601i | 62.9825 | + | 22.9237i | 9.23811 | − | 34.5062i |
5.8 | −2.54896 | − | 1.22590i | −1.62482 | − | 0.286499i | 4.99435 | + | 6.24952i | 2.82361 | − | 3.36505i | 3.79036 | + | 2.72213i | 13.2108 | + | 22.8819i | −5.06910 | − | 22.0523i | −22.8138 | − | 8.30353i | −11.3225 | + | 5.11590i |
5.9 | −2.50272 | − | 1.31772i | 8.78143 | + | 1.54840i | 4.52722 | + | 6.59578i | −6.43807 | + | 7.67259i | −19.9371 | − | 15.4467i | −1.25984 | − | 2.18211i | −2.63897 | − | 22.4730i | 49.3442 | + | 17.9598i | 26.2230 | − | 10.7188i |
5.10 | −2.49413 | − | 1.33392i | 4.10931 | + | 0.724583i | 4.44133 | + | 6.65392i | 9.57274 | − | 11.4084i | −9.28261 | − | 7.28868i | −5.68735 | − | 9.85077i | −2.20147 | − | 22.5201i | −9.01028 | − | 3.27947i | −39.0934 | + | 15.6846i |
5.11 | −2.41441 | + | 1.47330i | −2.55460 | − | 0.450445i | 3.65879 | − | 7.11430i | 0.869689 | − | 1.03646i | 6.83150 | − | 2.67612i | 9.58545 | + | 16.6025i | 1.64763 | + | 22.5674i | −19.0486 | − | 6.93313i | −0.572784 | + | 3.78374i |
5.12 | −2.34741 | + | 1.57787i | −4.63211 | − | 0.816766i | 3.02065 | − | 7.40781i | −0.297222 | + | 0.354215i | 12.1622 | − | 5.39159i | −12.9666 | − | 22.4588i | 4.59789 | + | 22.1553i | −4.58236 | − | 1.66784i | 0.138795 | − | 1.30047i |
5.13 | −2.22080 | + | 1.75159i | 6.31470 | + | 1.11345i | 1.86389 | − | 7.77984i | −13.6906 | + | 16.3158i | −15.9740 | + | 8.58799i | 2.50109 | + | 4.33202i | 9.48775 | + | 20.5422i | 13.2639 | + | 4.82767i | 1.82548 | − | 60.2142i |
5.14 | −2.19911 | − | 1.77874i | −5.54183 | − | 0.977174i | 1.67215 | + | 7.82329i | −10.2575 | + | 12.2244i | 10.4489 | + | 12.0064i | 7.83774 | + | 13.5754i | 10.2384 | − | 20.1786i | 4.38529 | + | 1.59612i | 44.3015 | − | 8.63736i |
5.15 | −2.00897 | − | 1.99099i | −4.45779 | − | 0.786029i | 0.0718986 | + | 7.99968i | 2.48844 | − | 2.96560i | 7.39058 | + | 10.4545i | −17.1535 | − | 29.7107i | 15.7829 | − | 16.2142i | −6.11761 | − | 2.22663i | −10.9037 | + | 1.00334i |
5.16 | −1.98788 | + | 2.01205i | 0.304087 | + | 0.0536187i | −0.0966730 | − | 7.99942i | 12.5870 | − | 15.0006i | −0.712371 | + | 0.505249i | −3.26800 | − | 5.66034i | 16.2874 | + | 15.7074i | −25.2821 | − | 9.20193i | 5.16049 | + | 55.1450i |
5.17 | −1.92911 | + | 2.06846i | 6.82434 | + | 1.20332i | −0.557038 | − | 7.98058i | 1.31007 | − | 1.56128i | −15.6539 | + | 11.7945i | −8.09624 | − | 14.0231i | 17.5821 | + | 14.2432i | 19.7520 | + | 7.18914i | 0.702169 | + | 5.72171i |
5.18 | −1.64798 | − | 2.29873i | −9.17013 | − | 1.61694i | −2.56833 | + | 7.57652i | 6.10344 | − | 7.27380i | 11.3953 | + | 23.7443i | 6.67659 | + | 11.5642i | 21.6489 | − | 6.58205i | 56.1051 | + | 20.4206i | −26.7789 | − | 2.04310i |
5.19 | −1.57035 | − | 2.35245i | 4.57945 | + | 0.807480i | −3.06800 | + | 7.38833i | −6.51289 | + | 7.76175i | −5.29178 | − | 12.0409i | 1.91022 | + | 3.30860i | 22.1985 | − | 4.38495i | −5.05239 | − | 1.83892i | 28.4866 | + | 3.13254i |
5.20 | −1.26778 | − | 2.52839i | 0.365686 | + | 0.0644802i | −4.78548 | + | 6.41087i | −4.71526 | + | 5.61942i | −0.300577 | − | 1.00634i | −3.17618 | − | 5.50130i | 22.2761 | + | 3.97197i | −25.2421 | − | 9.18738i | 20.1860 | + | 4.79781i |
See next 80 embeddings (of 348 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
8.b | even | 2 | 1 | inner |
19.e | even | 9 | 1 | inner |
152.t | even | 18 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 152.4.t.a | ✓ | 348 |
8.b | even | 2 | 1 | inner | 152.4.t.a | ✓ | 348 |
19.e | even | 9 | 1 | inner | 152.4.t.a | ✓ | 348 |
152.t | even | 18 | 1 | inner | 152.4.t.a | ✓ | 348 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
152.4.t.a | ✓ | 348 | 1.a | even | 1 | 1 | trivial |
152.4.t.a | ✓ | 348 | 8.b | even | 2 | 1 | inner |
152.4.t.a | ✓ | 348 | 19.e | even | 9 | 1 | inner |
152.4.t.a | ✓ | 348 | 152.t | even | 18 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(152, [\chi])\).