Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(949,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, 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("1900.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.g (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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 380) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
949.1 | 0 | −4.83157 | 0 | 0 | 0 | 3.72856i | 0 | 14.3441 | 0 | ||||||||||||||||||
949.2 | 0 | −4.83157 | 0 | 0 | 0 | − | 3.72856i | 0 | 14.3441 | 0 | |||||||||||||||||
949.3 | 0 | −3.53755 | 0 | 0 | 0 | − | 0.468611i | 0 | 3.51429 | 0 | |||||||||||||||||
949.4 | 0 | −3.53755 | 0 | 0 | 0 | 0.468611i | 0 | 3.51429 | 0 | ||||||||||||||||||
949.5 | 0 | −3.42504 | 0 | 0 | 0 | 9.18599i | 0 | 2.73093 | 0 | ||||||||||||||||||
949.6 | 0 | −3.42504 | 0 | 0 | 0 | − | 9.18599i | 0 | 2.73093 | 0 | |||||||||||||||||
949.7 | 0 | −3.14288 | 0 | 0 | 0 | 12.2192i | 0 | 0.877687 | 0 | ||||||||||||||||||
949.8 | 0 | −3.14288 | 0 | 0 | 0 | − | 12.2192i | 0 | 0.877687 | 0 | |||||||||||||||||
949.9 | 0 | −2.03369 | 0 | 0 | 0 | − | 4.27843i | 0 | −4.86411 | 0 | |||||||||||||||||
949.10 | 0 | −2.03369 | 0 | 0 | 0 | 4.27843i | 0 | −4.86411 | 0 | ||||||||||||||||||
949.11 | 0 | −0.630185 | 0 | 0 | 0 | 3.98530i | 0 | −8.60287 | 0 | ||||||||||||||||||
949.12 | 0 | −0.630185 | 0 | 0 | 0 | − | 3.98530i | 0 | −8.60287 | 0 | |||||||||||||||||
949.13 | 0 | 0.630185 | 0 | 0 | 0 | 3.98530i | 0 | −8.60287 | 0 | ||||||||||||||||||
949.14 | 0 | 0.630185 | 0 | 0 | 0 | − | 3.98530i | 0 | −8.60287 | 0 | |||||||||||||||||
949.15 | 0 | 2.03369 | 0 | 0 | 0 | − | 4.27843i | 0 | −4.86411 | 0 | |||||||||||||||||
949.16 | 0 | 2.03369 | 0 | 0 | 0 | 4.27843i | 0 | −4.86411 | 0 | ||||||||||||||||||
949.17 | 0 | 3.14288 | 0 | 0 | 0 | 12.2192i | 0 | 0.877687 | 0 | ||||||||||||||||||
949.18 | 0 | 3.14288 | 0 | 0 | 0 | − | 12.2192i | 0 | 0.877687 | 0 | |||||||||||||||||
949.19 | 0 | 3.42504 | 0 | 0 | 0 | 9.18599i | 0 | 2.73093 | 0 | ||||||||||||||||||
949.20 | 0 | 3.42504 | 0 | 0 | 0 | − | 9.18599i | 0 | 2.73093 | 0 | |||||||||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
5.b | even | 2 | 1 | inner |
19.b | odd | 2 | 1 | inner |
95.d | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1900.3.g.c | 24 | |
5.b | even | 2 | 1 | inner | 1900.3.g.c | 24 | |
5.c | odd | 4 | 1 | 380.3.e.a | ✓ | 12 | |
5.c | odd | 4 | 1 | 1900.3.e.f | 12 | ||
15.e | even | 4 | 1 | 3420.3.o.a | 12 | ||
19.b | odd | 2 | 1 | inner | 1900.3.g.c | 24 | |
20.e | even | 4 | 1 | 1520.3.h.b | 12 | ||
95.d | odd | 2 | 1 | inner | 1900.3.g.c | 24 | |
95.g | even | 4 | 1 | 380.3.e.a | ✓ | 12 | |
95.g | even | 4 | 1 | 1900.3.e.f | 12 | ||
285.j | odd | 4 | 1 | 3420.3.o.a | 12 | ||
380.j | odd | 4 | 1 | 1520.3.h.b | 12 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
380.3.e.a | ✓ | 12 | 5.c | odd | 4 | 1 | |
380.3.e.a | ✓ | 12 | 95.g | even | 4 | 1 | |
1520.3.h.b | 12 | 20.e | even | 4 | 1 | ||
1520.3.h.b | 12 | 380.j | odd | 4 | 1 | ||
1900.3.e.f | 12 | 5.c | odd | 4 | 1 | ||
1900.3.e.f | 12 | 95.g | even | 4 | 1 | ||
1900.3.g.c | 24 | 1.a | even | 1 | 1 | trivial | |
1900.3.g.c | 24 | 5.b | even | 2 | 1 | inner | |
1900.3.g.c | 24 | 19.b | odd | 2 | 1 | inner | |
1900.3.g.c | 24 | 95.d | odd | 2 | 1 | inner | |
3420.3.o.a | 12 | 15.e | even | 4 | 1 | ||
3420.3.o.a | 12 | 285.j | odd | 4 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{12} - 62T_{3}^{10} + 1445T_{3}^{8} - 15924T_{3}^{6} + 83244T_{3}^{4} - 170640T_{3}^{2} + 55600 \)
acting on \(S_{3}^{\mathrm{new}}(1900, [\chi])\).