Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (of order \(2\), degree \(1\), 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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
890.1 | − | 3.88526i | 0 | −11.0952 | 2.03195i | 0 | −5.71279 | 27.5669i | 0 | 7.89464 | |||||||||||||||||
890.2 | − | 3.86719i | 0 | −10.9551 | − | 9.44547i | 0 | 11.3204 | 26.8969i | 0 | −36.5274 | ||||||||||||||||
890.3 | − | 3.83653i | 0 | −10.7190 | 7.45843i | 0 | 0.844054 | 25.7776i | 0 | 28.6145 | |||||||||||||||||
890.4 | − | 3.66638i | 0 | −9.44232 | − | 0.851756i | 0 | 2.76278 | 19.9536i | 0 | −3.12286 | ||||||||||||||||
890.5 | − | 3.63886i | 0 | −9.24130 | − | 3.49336i | 0 | −9.62828 | 19.0724i | 0 | −12.7118 | ||||||||||||||||
890.6 | − | 3.62368i | 0 | −9.13107 | − | 3.89223i | 0 | −8.96960 | 18.5934i | 0 | −14.1042 | ||||||||||||||||
890.7 | − | 3.58466i | 0 | −8.84977 | − | 7.20639i | 0 | 4.70987 | 17.3848i | 0 | −25.8324 | ||||||||||||||||
890.8 | − | 3.57620i | 0 | −8.78923 | 5.13671i | 0 | 4.24305 | 17.1272i | 0 | 18.3699 | |||||||||||||||||
890.9 | − | 3.22737i | 0 | −6.41592 | 1.45400i | 0 | 2.15873 | 7.79707i | 0 | 4.69259 | |||||||||||||||||
890.10 | − | 3.21080i | 0 | −6.30922 | − | 0.600942i | 0 | 12.4847 | 7.41443i | 0 | −1.92950 | ||||||||||||||||
890.11 | − | 3.06240i | 0 | −5.37827 | − | 5.25232i | 0 | −2.64254 | 4.22081i | 0 | −16.0847 | ||||||||||||||||
890.12 | − | 3.03383i | 0 | −5.20412 | 9.69466i | 0 | −0.465658 | 3.65310i | 0 | 29.4119 | |||||||||||||||||
890.13 | − | 2.99230i | 0 | −4.95386 | 7.40706i | 0 | −4.26180 | 2.85423i | 0 | 22.1641 | |||||||||||||||||
890.14 | − | 2.96858i | 0 | −4.81247 | 3.90126i | 0 | 11.9179 | 2.41189i | 0 | 11.5812 | |||||||||||||||||
890.15 | − | 2.89430i | 0 | −4.37696 | 0.368899i | 0 | −11.4242 | 1.09103i | 0 | 1.06770 | |||||||||||||||||
890.16 | − | 2.71611i | 0 | −3.37726 | − | 6.95811i | 0 | 4.31599 | − | 1.69142i | 0 | −18.8990 | |||||||||||||||
890.17 | − | 2.56806i | 0 | −2.59492 | 0.662170i | 0 | −12.8177 | − | 3.60832i | 0 | 1.70049 | ||||||||||||||||
890.18 | − | 2.51986i | 0 | −2.34969 | 1.17863i | 0 | 3.92062 | − | 4.15855i | 0 | 2.96998 | ||||||||||||||||
890.19 | − | 2.47320i | 0 | −2.11671 | − | 7.47527i | 0 | −3.57682 | − | 4.65775i | 0 | −18.4878 | |||||||||||||||
890.20 | − | 2.40991i | 0 | −1.80767 | 4.01304i | 0 | −8.05053 | − | 5.28331i | 0 | 9.67106 | ||||||||||||||||
See all 84 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1143.3.b.a | ✓ | 84 |
3.b | odd | 2 | 1 | inner | 1143.3.b.a | ✓ | 84 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1143.3.b.a | ✓ | 84 | 1.a | even | 1 | 1 | trivial |
1143.3.b.a | ✓ | 84 | 3.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1143, [\chi])\).