Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,3,Mod(736,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.736");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(31.4714705336\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
736.1 | − | 3.97461i | −1.73205 | −11.7975 | −2.23607 | 6.88422i | 2.64575i | 30.9920i | 3.00000 | 8.88749i | |||||||||||||||||
736.2 | − | 3.80731i | −1.73205 | −10.4956 | −2.23607 | 6.59446i | − | 2.64575i | 24.7309i | 3.00000 | 8.51341i | ||||||||||||||||
736.3 | − | 3.79404i | 1.73205 | −10.3948 | 2.23607 | − | 6.57148i | − | 2.64575i | 24.2621i | 3.00000 | − | 8.48374i | ||||||||||||||
736.4 | − | 3.73924i | 1.73205 | −9.98188 | −2.23607 | − | 6.47655i | − | 2.64575i | 22.3677i | 3.00000 | 8.36118i | |||||||||||||||
736.5 | − | 3.73084i | −1.73205 | −9.91918 | 2.23607 | 6.46201i | − | 2.64575i | 22.0835i | 3.00000 | − | 8.34242i | |||||||||||||||
736.6 | − | 3.67613i | 1.73205 | −9.51395 | −2.23607 | − | 6.36725i | 2.64575i | 20.2700i | 3.00000 | 8.22008i | ||||||||||||||||
736.7 | − | 3.66479i | −1.73205 | −9.43072 | 2.23607 | 6.34761i | − | 2.64575i | 19.9025i | 3.00000 | − | 8.19473i | |||||||||||||||
736.8 | − | 3.64908i | 1.73205 | −9.31580 | 2.23607 | − | 6.32039i | 2.64575i | 19.3978i | 3.00000 | − | 8.15959i | |||||||||||||||
736.9 | − | 3.57619i | −1.73205 | −8.78910 | 2.23607 | 6.19413i | 2.64575i | 17.1267i | 3.00000 | − | 7.99659i | ||||||||||||||||
736.10 | − | 3.57202i | 1.73205 | −8.75932 | −2.23607 | − | 6.18692i | − | 2.64575i | 17.0004i | 3.00000 | 7.98728i | |||||||||||||||
736.11 | − | 3.29262i | 1.73205 | −6.84133 | 2.23607 | − | 5.70298i | − | 2.64575i | 9.35542i | 3.00000 | − | 7.36252i | ||||||||||||||
736.12 | − | 3.27785i | −1.73205 | −6.74433 | −2.23607 | 5.67741i | − | 2.64575i | 8.99550i | 3.00000 | 7.32950i | ||||||||||||||||
736.13 | − | 3.25995i | 1.73205 | −6.62729 | 2.23607 | − | 5.64640i | 2.64575i | 8.56486i | 3.00000 | − | 7.28948i | |||||||||||||||
736.14 | − | 2.97479i | 1.73205 | −4.84935 | 2.23607 | − | 5.15248i | − | 2.64575i | 2.52665i | 3.00000 | − | 6.65182i | ||||||||||||||
736.15 | − | 2.94196i | 1.73205 | −4.65512 | −2.23607 | − | 5.09562i | 2.64575i | 1.92733i | 3.00000 | 6.57842i | ||||||||||||||||
736.16 | − | 2.91962i | −1.73205 | −4.52416 | 2.23607 | 5.05692i | 2.64575i | 1.53034i | 3.00000 | − | 6.52846i | ||||||||||||||||
736.17 | − | 2.91387i | −1.73205 | −4.49063 | 2.23607 | 5.04697i | − | 2.64575i | 1.42964i | 3.00000 | − | 6.51561i | |||||||||||||||
736.18 | − | 2.89693i | −1.73205 | −4.39221 | 2.23607 | 5.01763i | 2.64575i | 1.13621i | 3.00000 | − | 6.47774i | ||||||||||||||||
736.19 | − | 2.81721i | −1.73205 | −3.93666 | −2.23607 | 4.87955i | 2.64575i | − | 0.178435i | 3.00000 | 6.29947i | ||||||||||||||||
736.20 | − | 2.77171i | −1.73205 | −3.68240 | −2.23607 | 4.80075i | − | 2.64575i | − | 0.880291i | 3.00000 | 6.19774i | |||||||||||||||
See all 96 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
11.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1155.3.b.a | ✓ | 96 |
11.b | odd | 2 | 1 | inner | 1155.3.b.a | ✓ | 96 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1155.3.b.a | ✓ | 96 | 1.a | even | 1 | 1 | trivial |
1155.3.b.a | ✓ | 96 | 11.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1155, [\chi])\).