Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(10,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 11, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.10");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.bf (of order \(66\), degree \(20\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(640\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{66})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{66}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
10.1 | −0.853118 | + | 2.46492i | 0.458227 | + | 0.888835i | −3.77593 | − | 2.96942i | −2.73649 | + | 0.261303i | −2.58183 | + | 0.371212i | 0.617353 | + | 2.57272i | 6.15210 | − | 3.95371i | −0.580057 | + | 0.814576i | 1.69045 | − | 6.96815i |
10.2 | −0.850716 | + | 2.45798i | −0.458227 | − | 0.888835i | −3.74585 | − | 2.94577i | 1.41466 | − | 0.135083i | 2.57456 | − | 0.370166i | −1.58058 | + | 2.12174i | 6.05103 | − | 3.88876i | −0.580057 | + | 0.814576i | −0.871437 | + | 3.59211i |
10.3 | −0.838936 | + | 2.42395i | −0.458227 | − | 0.888835i | −3.59960 | − | 2.83076i | −2.60640 | + | 0.248881i | 2.53891 | − | 0.365041i | 2.49779 | − | 0.872377i | 5.56577 | − | 3.57691i | −0.580057 | + | 0.814576i | 1.58333 | − | 6.52656i |
10.4 | −0.797371 | + | 2.30385i | 0.458227 | + | 0.888835i | −3.09983 | − | 2.43773i | 1.48893 | − | 0.142176i | −2.41312 | + | 0.346955i | 2.64327 | + | 0.114618i | 3.98605 | − | 2.56168i | −0.580057 | + | 0.814576i | −0.859680 | + | 3.54365i |
10.5 | −0.647644 | + | 1.87125i | 0.458227 | + | 0.888835i | −1.51001 | − | 1.18748i | −3.91898 | + | 0.374217i | −1.96000 | + | 0.281805i | −1.01941 | − | 2.44148i | −0.131596 | + | 0.0845715i | −0.580057 | + | 0.814576i | 1.83785 | − | 7.57573i |
10.6 | −0.643746 | + | 1.85998i | −0.458227 | − | 0.888835i | −1.47302 | − | 1.15839i | 2.63722 | − | 0.251824i | 1.94820 | − | 0.280109i | −0.893381 | − | 2.49036i | −0.208726 | + | 0.134140i | −0.580057 | + | 0.814576i | −1.22931 | + | 5.06730i |
10.7 | −0.632527 | + | 1.82757i | 0.458227 | + | 0.888835i | −1.36781 | − | 1.07566i | 0.843558 | − | 0.0805501i | −1.91425 | + | 0.275227i | −2.38264 | + | 1.15022i | −0.422845 | + | 0.271746i | −0.580057 | + | 0.814576i | −0.386363 | + | 1.59261i |
10.8 | −0.544288 | + | 1.57262i | −0.458227 | − | 0.888835i | −0.604770 | − | 0.475596i | 1.92390 | − | 0.183711i | 1.64721 | − | 0.236832i | 0.763953 | + | 2.53306i | −1.72283 | + | 1.10720i | −0.580057 | + | 0.814576i | −0.758252 | + | 3.12556i |
10.9 | −0.473440 | + | 1.36792i | −0.458227 | − | 0.888835i | −0.0749403 | − | 0.0589337i | −1.20704 | + | 0.115258i | 1.43279 | − | 0.206005i | 0.607831 | − | 2.57498i | −2.31938 | + | 1.49058i | −0.580057 | + | 0.814576i | 0.413798 | − | 1.70570i |
10.10 | −0.340926 | + | 0.985040i | 0.458227 | + | 0.888835i | 0.718033 | + | 0.564667i | 3.21073 | − | 0.306587i | −1.03176 | + | 0.148345i | −1.39165 | − | 2.25018i | −2.55481 | + | 1.64188i | −0.580057 | + | 0.814576i | −0.792618 | + | 3.26722i |
10.11 | −0.319328 | + | 0.922636i | 0.458227 | + | 0.888835i | 0.822819 | + | 0.647072i | 2.77405 | − | 0.264890i | −0.966396 | + | 0.138947i | 1.16682 | + | 2.37456i | −2.50245 | + | 1.60823i | −0.580057 | + | 0.814576i | −0.641435 | + | 2.64403i |
10.12 | −0.311023 | + | 0.898642i | −0.458227 | − | 0.888835i | 0.861285 | + | 0.677322i | −1.14736 | + | 0.109560i | 0.941264 | − | 0.135333i | −2.64155 | − | 0.149090i | −2.47652 | + | 1.59156i | −0.580057 | + | 0.814576i | 0.258401 | − | 1.06514i |
10.13 | −0.184479 | + | 0.533017i | 0.458227 | + | 0.888835i | 1.32203 | + | 1.03966i | −3.44259 | + | 0.328727i | −0.558297 | + | 0.0802710i | 0.528452 | + | 2.59244i | −1.74704 | + | 1.12275i | −0.580057 | + | 0.814576i | 0.459867 | − | 1.89560i |
10.14 | −0.175281 | + | 0.506440i | 0.458227 | + | 0.888835i | 1.34635 | + | 1.05878i | −1.28396 | + | 0.122604i | −0.530461 | + | 0.0762687i | 2.45236 | − | 0.992951i | −1.67388 | + | 1.07574i | −0.580057 | + | 0.814576i | 0.162963 | − | 0.671742i |
10.15 | −0.131204 | + | 0.379090i | −0.458227 | − | 0.888835i | 1.44561 | + | 1.13684i | 3.76955 | − | 0.359949i | 0.397070 | − | 0.0570900i | 2.39754 | − | 1.11885i | −1.29558 | + | 0.832618i | −0.580057 | + | 0.814576i | −0.358129 | + | 1.47623i |
10.16 | −0.0815859 | + | 0.235727i | −0.458227 | − | 0.888835i | 1.52320 | + | 1.19785i | −1.53664 | + | 0.146731i | 0.246907 | − | 0.0354999i | −2.59838 | − | 0.498437i | −0.826333 | + | 0.531052i | −0.580057 | + | 0.814576i | 0.0907797 | − | 0.374199i |
10.17 | 0.0478877 | − | 0.138362i | 0.458227 | + | 0.888835i | 1.55526 | + | 1.22307i | −2.41931 | + | 0.231016i | 0.144925 | − | 0.0208370i | −2.60435 | + | 0.466234i | 0.490049 | − | 0.314935i | −0.580057 | + | 0.814576i | −0.0838914 | + | 0.345805i |
10.18 | 0.0503654 | − | 0.145521i | −0.458227 | − | 0.888835i | 1.55347 | + | 1.22166i | −3.87542 | + | 0.370058i | −0.152423 | + | 0.0219152i | 2.22141 | − | 1.43713i | 0.515109 | − | 0.331040i | −0.580057 | + | 0.814576i | −0.141336 | + | 0.582594i |
10.19 | 0.0597980 | − | 0.172775i | −0.458227 | − | 0.888835i | 1.54583 | + | 1.21565i | 0.371368 | − | 0.0354614i | −0.180970 | + | 0.0260195i | 1.77822 | + | 1.95906i | 0.610086 | − | 0.392079i | −0.580057 | + | 0.814576i | 0.0160803 | − | 0.0662837i |
10.20 | 0.114790 | − | 0.331663i | 0.458227 | + | 0.888835i | 1.47528 | + | 1.16017i | 0.530378 | − | 0.0506450i | 0.347394 | − | 0.0499477i | 0.390363 | − | 2.61680i | 1.14464 | − | 0.735614i | −0.580057 | + | 0.814576i | 0.0440849 | − | 0.181721i |
See next 80 embeddings (of 640 total) |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.d | odd | 6 | 1 | inner |
23.d | odd | 22 | 1 | inner |
161.o | even | 66 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 483.2.bf.a | ✓ | 640 |
7.d | odd | 6 | 1 | inner | 483.2.bf.a | ✓ | 640 |
23.d | odd | 22 | 1 | inner | 483.2.bf.a | ✓ | 640 |
161.o | even | 66 | 1 | inner | 483.2.bf.a | ✓ | 640 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
483.2.bf.a | ✓ | 640 | 1.a | even | 1 | 1 | trivial |
483.2.bf.a | ✓ | 640 | 7.d | odd | 6 | 1 | inner |
483.2.bf.a | ✓ | 640 | 23.d | odd | 22 | 1 | inner |
483.2.bf.a | ✓ | 640 | 161.o | even | 66 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(483, [\chi])\).