Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5796,2,Mod(5473,5796)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5796, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5796.5473");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5796.k (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: | \(46.2812930115\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5473.1 | 0 | 0 | 0 | −3.79323 | 0 | −2.36332 | − | 1.18943i | 0 | 0 | 0 | ||||||||||||||||
5473.2 | 0 | 0 | 0 | −3.79323 | 0 | 2.36332 | − | 1.18943i | 0 | 0 | 0 | ||||||||||||||||
5473.3 | 0 | 0 | 0 | −3.79323 | 0 | 2.36332 | + | 1.18943i | 0 | 0 | 0 | ||||||||||||||||
5473.4 | 0 | 0 | 0 | −3.79323 | 0 | −2.36332 | + | 1.18943i | 0 | 0 | 0 | ||||||||||||||||
5473.5 | 0 | 0 | 0 | −3.00417 | 0 | 1.13593 | + | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.6 | 0 | 0 | 0 | −3.00417 | 0 | −1.13593 | + | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.7 | 0 | 0 | 0 | −3.00417 | 0 | −1.13593 | − | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.8 | 0 | 0 | 0 | −3.00417 | 0 | 1.13593 | − | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.9 | 0 | 0 | 0 | −1.25950 | 0 | 0.790195 | + | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.10 | 0 | 0 | 0 | −1.25950 | 0 | −0.790195 | − | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.11 | 0 | 0 | 0 | −1.25950 | 0 | −0.790195 | + | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.12 | 0 | 0 | 0 | −1.25950 | 0 | 0.790195 | − | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.13 | 0 | 0 | 0 | 1.25950 | 0 | −0.790195 | − | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.14 | 0 | 0 | 0 | 1.25950 | 0 | 0.790195 | − | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.15 | 0 | 0 | 0 | 1.25950 | 0 | 0.790195 | + | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.16 | 0 | 0 | 0 | 1.25950 | 0 | −0.790195 | + | 2.52499i | 0 | 0 | 0 | ||||||||||||||||
5473.17 | 0 | 0 | 0 | 3.00417 | 0 | −1.13593 | − | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.18 | 0 | 0 | 0 | 3.00417 | 0 | 1.13593 | − | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.19 | 0 | 0 | 0 | 3.00417 | 0 | 1.13593 | + | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
5473.20 | 0 | 0 | 0 | 3.00417 | 0 | −1.13593 | + | 2.38949i | 0 | 0 | 0 | ||||||||||||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
7.b | odd | 2 | 1 | inner |
21.c | even | 2 | 1 | inner |
23.b | odd | 2 | 1 | inner |
69.c | even | 2 | 1 | inner |
161.c | even | 2 | 1 | inner |
483.c | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 5796.2.k.c | ✓ | 24 |
3.b | odd | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
7.b | odd | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
21.c | even | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
23.b | odd | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
69.c | even | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
161.c | even | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
483.c | odd | 2 | 1 | inner | 5796.2.k.c | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
5796.2.k.c | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
5796.2.k.c | ✓ | 24 | 3.b | odd | 2 | 1 | inner |
5796.2.k.c | ✓ | 24 | 7.b | odd | 2 | 1 | inner |
5796.2.k.c | ✓ | 24 | 21.c | even | 2 | 1 | inner |
5796.2.k.c | ✓ | 24 | 23.b | odd | 2 | 1 | inner |
5796.2.k.c | ✓ | 24 | 69.c | even | 2 | 1 | inner |
5796.2.k.c | ✓ | 24 | 161.c | even | 2 | 1 | inner |
5796.2.k.c | ✓ | 24 | 483.c | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{6} - 25T_{5}^{4} + 167T_{5}^{2} - 206 \)
acting on \(S_{2}^{\mathrm{new}}(5796, [\chi])\).