Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2790,2,Mod(2231,2790)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2790, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2790.2231");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2790.h (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: | \(22.2782621639\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2231.1 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | −4.03497 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.2 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | −4.03497 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.3 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | 3.43954 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.4 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | 3.43954 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.5 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | −4.03497 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.6 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | −4.03497 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.7 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | −2.02860 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.8 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | −2.02860 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.9 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | 1.59543 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.10 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | 1.59543 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.11 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | 3.43954 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.12 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | 3.43954 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.13 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | −0.792404 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.14 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | −0.792404 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.15 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | 3.82100 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.16 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | 3.82100 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.17 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | −0.792404 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.18 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | −0.792404 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
2231.19 | − | 1.00000i | 0 | −1.00000 | 1.00000i | 0 | −2.02860 | 1.00000i | 0 | 1.00000 | |||||||||||||||||
2231.20 | 1.00000i | 0 | −1.00000 | − | 1.00000i | 0 | −2.02860 | − | 1.00000i | 0 | 1.00000 | ||||||||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
31.b | odd | 2 | 1 | inner |
93.c | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2790.2.h.b | ✓ | 24 |
3.b | odd | 2 | 1 | inner | 2790.2.h.b | ✓ | 24 |
31.b | odd | 2 | 1 | inner | 2790.2.h.b | ✓ | 24 |
93.c | even | 2 | 1 | inner | 2790.2.h.b | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2790.2.h.b | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
2790.2.h.b | ✓ | 24 | 3.b | odd | 2 | 1 | inner |
2790.2.h.b | ✓ | 24 | 31.b | odd | 2 | 1 | inner |
2790.2.h.b | ✓ | 24 | 93.c | even | 2 | 1 | inner |