Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(881,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.881");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.h (of order \(2\), degree \(1\), not 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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 56) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
881.1 | 0 | −5.56010 | 0 | −3.05841 | 0 | 0 | 0 | 21.9148 | 0 | ||||||||||||||||||
881.2 | 0 | −5.56010 | 0 | −3.05841 | 0 | 0 | 0 | 21.9148 | 0 | ||||||||||||||||||
881.3 | 0 | −3.89635 | 0 | 8.85969 | 0 | 0 | 0 | 6.18155 | 0 | ||||||||||||||||||
881.4 | 0 | −3.89635 | 0 | 8.85969 | 0 | 0 | 0 | 6.18155 | 0 | ||||||||||||||||||
881.5 | 0 | −3.86988 | 0 | 4.67764 | 0 | 0 | 0 | 5.97596 | 0 | ||||||||||||||||||
881.6 | 0 | −3.86988 | 0 | 4.67764 | 0 | 0 | 0 | 5.97596 | 0 | ||||||||||||||||||
881.7 | 0 | −3.40276 | 0 | −4.31716 | 0 | 0 | 0 | 2.57876 | 0 | ||||||||||||||||||
881.8 | 0 | −3.40276 | 0 | −4.31716 | 0 | 0 | 0 | 2.57876 | 0 | ||||||||||||||||||
881.9 | 0 | −2.33563 | 0 | −3.10110 | 0 | 0 | 0 | −3.54484 | 0 | ||||||||||||||||||
881.10 | 0 | −2.33563 | 0 | −3.10110 | 0 | 0 | 0 | −3.54484 | 0 | ||||||||||||||||||
881.11 | 0 | −0.910863 | 0 | −6.34503 | 0 | 0 | 0 | −8.17033 | 0 | ||||||||||||||||||
881.12 | 0 | −0.910863 | 0 | −6.34503 | 0 | 0 | 0 | −8.17033 | 0 | ||||||||||||||||||
881.13 | 0 | −0.253256 | 0 | −3.57178 | 0 | 0 | 0 | −8.93586 | 0 | ||||||||||||||||||
881.14 | 0 | −0.253256 | 0 | −3.57178 | 0 | 0 | 0 | −8.93586 | 0 | ||||||||||||||||||
881.15 | 0 | 0.253256 | 0 | 3.57178 | 0 | 0 | 0 | −8.93586 | 0 | ||||||||||||||||||
881.16 | 0 | 0.253256 | 0 | 3.57178 | 0 | 0 | 0 | −8.93586 | 0 | ||||||||||||||||||
881.17 | 0 | 0.910863 | 0 | 6.34503 | 0 | 0 | 0 | −8.17033 | 0 | ||||||||||||||||||
881.18 | 0 | 0.910863 | 0 | 6.34503 | 0 | 0 | 0 | −8.17033 | 0 | ||||||||||||||||||
881.19 | 0 | 2.33563 | 0 | 3.10110 | 0 | 0 | 0 | −3.54484 | 0 | ||||||||||||||||||
881.20 | 0 | 2.33563 | 0 | 3.10110 | 0 | 0 | 0 | −3.54484 | 0 | ||||||||||||||||||
See all 28 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.b | odd | 2 | 1 | inner |
8.b | even | 2 | 1 | inner |
56.h | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1568.3.h.a | 28 | |
4.b | odd | 2 | 1 | 392.3.h.a | 28 | ||
7.b | odd | 2 | 1 | inner | 1568.3.h.a | 28 | |
7.c | even | 3 | 1 | 224.3.n.a | 28 | ||
7.d | odd | 6 | 1 | 224.3.n.a | 28 | ||
8.b | even | 2 | 1 | inner | 1568.3.h.a | 28 | |
8.d | odd | 2 | 1 | 392.3.h.a | 28 | ||
28.d | even | 2 | 1 | 392.3.h.a | 28 | ||
28.f | even | 6 | 1 | 56.3.j.a | ✓ | 28 | |
28.f | even | 6 | 1 | 392.3.j.e | 28 | ||
28.g | odd | 6 | 1 | 56.3.j.a | ✓ | 28 | |
28.g | odd | 6 | 1 | 392.3.j.e | 28 | ||
56.e | even | 2 | 1 | 392.3.h.a | 28 | ||
56.h | odd | 2 | 1 | inner | 1568.3.h.a | 28 | |
56.j | odd | 6 | 1 | 224.3.n.a | 28 | ||
56.k | odd | 6 | 1 | 56.3.j.a | ✓ | 28 | |
56.k | odd | 6 | 1 | 392.3.j.e | 28 | ||
56.m | even | 6 | 1 | 56.3.j.a | ✓ | 28 | |
56.m | even | 6 | 1 | 392.3.j.e | 28 | ||
56.p | even | 6 | 1 | 224.3.n.a | 28 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
56.3.j.a | ✓ | 28 | 28.f | even | 6 | 1 | |
56.3.j.a | ✓ | 28 | 28.g | odd | 6 | 1 | |
56.3.j.a | ✓ | 28 | 56.k | odd | 6 | 1 | |
56.3.j.a | ✓ | 28 | 56.m | even | 6 | 1 | |
224.3.n.a | 28 | 7.c | even | 3 | 1 | ||
224.3.n.a | 28 | 7.d | odd | 6 | 1 | ||
224.3.n.a | 28 | 56.j | odd | 6 | 1 | ||
224.3.n.a | 28 | 56.p | even | 6 | 1 | ||
392.3.h.a | 28 | 4.b | odd | 2 | 1 | ||
392.3.h.a | 28 | 8.d | odd | 2 | 1 | ||
392.3.h.a | 28 | 28.d | even | 2 | 1 | ||
392.3.h.a | 28 | 56.e | even | 2 | 1 | ||
392.3.j.e | 28 | 28.f | even | 6 | 1 | ||
392.3.j.e | 28 | 28.g | odd | 6 | 1 | ||
392.3.j.e | 28 | 56.k | odd | 6 | 1 | ||
392.3.j.e | 28 | 56.m | even | 6 | 1 | ||
1568.3.h.a | 28 | 1.a | even | 1 | 1 | trivial | |
1568.3.h.a | 28 | 7.b | odd | 2 | 1 | inner | |
1568.3.h.a | 28 | 8.b | even | 2 | 1 | inner | |
1568.3.h.a | 28 | 56.h | odd | 2 | 1 | inner |