Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,5,Mod(91,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
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("115.91");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.d (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: | \(11.8875457546\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
91.1 | −7.34406 | 5.90949 | 37.9353 | − | 11.1803i | −43.3996 | − | 48.6157i | −161.094 | −46.0780 | 82.1091i | ||||||||||||||||
91.2 | −7.34406 | 5.90949 | 37.9353 | 11.1803i | −43.3996 | 48.6157i | −161.094 | −46.0780 | − | 82.1091i | |||||||||||||||||
91.3 | −6.41480 | −5.40062 | 25.1496 | − | 11.1803i | 34.6439 | 39.9461i | −58.6931 | −51.8333 | 71.7196i | |||||||||||||||||
91.4 | −6.41480 | −5.40062 | 25.1496 | 11.1803i | 34.6439 | − | 39.9461i | −58.6931 | −51.8333 | − | 71.7196i | ||||||||||||||||
91.5 | −5.83518 | 15.5811 | 18.0493 | − | 11.1803i | −90.9187 | 44.9289i | −11.9583 | 161.771 | 65.2393i | |||||||||||||||||
91.6 | −5.83518 | 15.5811 | 18.0493 | 11.1803i | −90.9187 | − | 44.9289i | −11.9583 | 161.771 | − | 65.2393i | ||||||||||||||||
91.7 | −4.68831 | −9.45649 | 5.98022 | − | 11.1803i | 44.3349 | 28.1385i | 46.9758 | 8.42527 | 52.4169i | |||||||||||||||||
91.8 | −4.68831 | −9.45649 | 5.98022 | 11.1803i | 44.3349 | − | 28.1385i | 46.9758 | 8.42527 | − | 52.4169i | ||||||||||||||||
91.9 | −3.39557 | −16.6588 | −4.47013 | − | 11.1803i | 56.5661 | − | 77.4058i | 69.5077 | 196.516 | 37.9636i | ||||||||||||||||
91.10 | −3.39557 | −16.6588 | −4.47013 | 11.1803i | 56.5661 | 77.4058i | 69.5077 | 196.516 | − | 37.9636i | |||||||||||||||||
91.11 | −3.11306 | 8.30828 | −6.30887 | − | 11.1803i | −25.8642 | 6.01095i | 69.4488 | −11.9725 | 34.8050i | |||||||||||||||||
91.12 | −3.11306 | 8.30828 | −6.30887 | 11.1803i | −25.8642 | − | 6.01095i | 69.4488 | −11.9725 | − | 34.8050i | ||||||||||||||||
91.13 | −1.17931 | −3.23146 | −14.6092 | − | 11.1803i | 3.81090 | − | 21.2126i | 36.0979 | −70.5577 | 13.1851i | ||||||||||||||||
91.14 | −1.17931 | −3.23146 | −14.6092 | 11.1803i | 3.81090 | 21.2126i | 36.0979 | −70.5577 | − | 13.1851i | |||||||||||||||||
91.15 | −0.753970 | 13.3391 | −15.4315 | − | 11.1803i | −10.0573 | 4.37200i | 23.6984 | 96.9319 | 8.42964i | |||||||||||||||||
91.16 | −0.753970 | 13.3391 | −15.4315 | 11.1803i | −10.0573 | − | 4.37200i | 23.6984 | 96.9319 | − | 8.42964i | ||||||||||||||||
91.17 | 2.18924 | 6.68855 | −11.2072 | − | 11.1803i | 14.6428 | 94.1703i | −59.5631 | −36.2633 | − | 24.4764i | ||||||||||||||||
91.18 | 2.18924 | 6.68855 | −11.2072 | 11.1803i | 14.6428 | − | 94.1703i | −59.5631 | −36.2633 | 24.4764i | |||||||||||||||||
91.19 | 2.62865 | 4.08866 | −9.09019 | − | 11.1803i | 10.7477 | − | 56.7651i | −65.9534 | −64.2829 | − | 29.3892i | |||||||||||||||
91.20 | 2.62865 | 4.08866 | −9.09019 | 11.1803i | 10.7477 | 56.7651i | −65.9534 | −64.2829 | 29.3892i | ||||||||||||||||||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
23.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 115.5.d.a | ✓ | 32 |
23.b | odd | 2 | 1 | inner | 115.5.d.a | ✓ | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
115.5.d.a | ✓ | 32 | 1.a | even | 1 | 1 | trivial |
115.5.d.a | ✓ | 32 | 23.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(115, [\chi])\).