Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [95,11,Mod(56,95)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(95, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("95.56");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.c (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: | \(60.3589390040\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
56.1 | − | 62.1919i | − | 381.522i | −2843.84 | −1397.54 | −23727.6 | −5606.85 | 113179.i | −86509.7 | 86915.9i | ||||||||||||||||
56.2 | − | 61.7537i | − | 249.725i | −2789.52 | 1397.54 | −15421.4 | 30173.4 | 109028.i | −3313.41 | − | 86303.5i | |||||||||||||||
56.3 | − | 59.8034i | 69.3732i | −2552.45 | −1397.54 | 4148.75 | −21925.2 | 91406.6i | 54236.4 | 83577.8i | |||||||||||||||||
56.4 | − | 59.4439i | 262.238i | −2509.58 | 1397.54 | 15588.5 | 13097.9 | 88308.7i | −9719.86 | − | 83075.4i | ||||||||||||||||
56.5 | − | 58.8412i | 322.019i | −2438.29 | 1397.54 | 18948.0 | −14394.2 | 83218.3i | −44647.2 | − | 82233.1i | ||||||||||||||||
56.6 | − | 56.3762i | 430.055i | −2154.27 | −1397.54 | 24244.8 | 15010.3 | 63720.6i | −125898. | 78788.1i | |||||||||||||||||
56.7 | − | 55.5930i | − | 228.918i | −2066.58 | 1397.54 | −12726.3 | −20724.8 | 57960.4i | 6645.37 | − | 77693.6i | |||||||||||||||
56.8 | − | 52.8152i | − | 180.092i | −1765.45 | −1397.54 | −9511.57 | 22409.1 | 39159.6i | 26616.0 | 73811.5i | ||||||||||||||||
56.9 | − | 49.9636i | 275.923i | −1472.36 | −1397.54 | 13786.1 | 451.343 | 22401.8i | −17084.7 | 69826.3i | |||||||||||||||||
56.10 | − | 49.5166i | − | 99.2692i | −1427.90 | 1397.54 | −4915.48 | −5912.68 | 19999.7i | 49194.6 | − | 69201.6i | |||||||||||||||
56.11 | − | 49.4757i | 10.8416i | −1423.84 | −1397.54 | 536.394 | 13282.9 | 19782.5i | 58931.5 | 69144.4i | |||||||||||||||||
56.12 | − | 45.0974i | 233.570i | −1009.78 | 1397.54 | 10533.4 | 29576.4 | − | 641.391i | 4493.86 | − | 63025.6i | |||||||||||||||
56.13 | − | 44.6372i | − | 337.722i | −968.483 | −1397.54 | −15075.0 | −20874.9 | − | 2478.12i | −55007.3 | 62382.4i | |||||||||||||||
56.14 | − | 42.8761i | − | 436.600i | −814.356 | 1397.54 | −18719.7 | 16685.1 | − | 8988.69i | −131571. | − | 59921.1i | ||||||||||||||
56.15 | − | 42.0113i | 256.740i | −740.946 | 1397.54 | 10786.0 | −9164.39 | − | 11891.4i | −6866.66 | − | 58712.5i | |||||||||||||||
56.16 | − | 40.7068i | 92.7742i | −633.046 | −1397.54 | 3776.54 | −29798.5 | − | 15914.5i | 50441.9 | 56889.5i | ||||||||||||||||
56.17 | − | 39.1187i | − | 305.024i | −506.271 | −1397.54 | −11932.1 | 11384.7 | − | 20252.9i | −33990.7 | 54670.0i | |||||||||||||||
56.18 | − | 32.6481i | 41.6316i | −41.8959 | 1397.54 | 1359.19 | −15608.7 | − | 32063.8i | 57315.8 | − | 45627.1i | |||||||||||||||
56.19 | − | 30.4924i | 355.876i | 94.2110 | −1397.54 | 10851.5 | −1797.03 | − | 34097.0i | −67598.8 | 42614.5i | ||||||||||||||||
56.20 | − | 29.0491i | 463.924i | 180.148 | 1397.54 | 13476.6 | 20091.2 | − | 34979.5i | −156176. | − | 40597.4i | |||||||||||||||
See all 68 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 95.11.c.a | ✓ | 68 |
19.b | odd | 2 | 1 | inner | 95.11.c.a | ✓ | 68 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
95.11.c.a | ✓ | 68 | 1.a | even | 1 | 1 | trivial |
95.11.c.a | ✓ | 68 | 19.b | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(95, [\chi])\).