Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,3,Mod(573,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, 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("1148.573");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.g (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: | \(31.2807343486\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
573.1 | 0 | −5.69634 | 0 | − | 3.03689i | 0 | 4.13999 | + | 5.64451i | 0 | 23.4483 | 0 | |||||||||||||||
573.2 | 0 | −5.69634 | 0 | 3.03689i | 0 | 4.13999 | − | 5.64451i | 0 | 23.4483 | 0 | ||||||||||||||||
573.3 | 0 | −4.89631 | 0 | − | 0.632775i | 0 | −4.64857 | + | 5.23362i | 0 | 14.9739 | 0 | |||||||||||||||
573.4 | 0 | −4.89631 | 0 | 0.632775i | 0 | −4.64857 | − | 5.23362i | 0 | 14.9739 | 0 | ||||||||||||||||
573.5 | 0 | −4.85691 | 0 | − | 8.72459i | 0 | −6.81335 | − | 1.60571i | 0 | 14.5896 | 0 | |||||||||||||||
573.6 | 0 | −4.85691 | 0 | 8.72459i | 0 | −6.81335 | + | 1.60571i | 0 | 14.5896 | 0 | ||||||||||||||||
573.7 | 0 | −4.83467 | 0 | − | 5.66595i | 0 | 5.53034 | + | 4.29131i | 0 | 14.3740 | 0 | |||||||||||||||
573.8 | 0 | −4.83467 | 0 | 5.66595i | 0 | 5.53034 | − | 4.29131i | 0 | 14.3740 | 0 | ||||||||||||||||
573.9 | 0 | −3.63578 | 0 | − | 6.01754i | 0 | 3.80993 | − | 5.87235i | 0 | 4.21887 | 0 | |||||||||||||||
573.10 | 0 | −3.63578 | 0 | 6.01754i | 0 | 3.80993 | + | 5.87235i | 0 | 4.21887 | 0 | ||||||||||||||||
573.11 | 0 | −3.47135 | 0 | 3.69792i | 0 | −2.49537 | + | 6.54012i | 0 | 3.05028 | 0 | ||||||||||||||||
573.12 | 0 | −3.47135 | 0 | − | 3.69792i | 0 | −2.49537 | − | 6.54012i | 0 | 3.05028 | 0 | |||||||||||||||
573.13 | 0 | −3.09735 | 0 | 5.69702i | 0 | 5.23661 | + | 4.64521i | 0 | 0.593579 | 0 | ||||||||||||||||
573.14 | 0 | −3.09735 | 0 | − | 5.69702i | 0 | 5.23661 | − | 4.64521i | 0 | 0.593579 | 0 | |||||||||||||||
573.15 | 0 | −2.46507 | 0 | − | 5.99343i | 0 | −6.99216 | − | 0.331276i | 0 | −2.92345 | 0 | |||||||||||||||
573.16 | 0 | −2.46507 | 0 | 5.99343i | 0 | −6.99216 | + | 0.331276i | 0 | −2.92345 | 0 | ||||||||||||||||
573.17 | 0 | −2.31144 | 0 | 3.75379i | 0 | 6.99996 | − | 0.0226023i | 0 | −3.65724 | 0 | ||||||||||||||||
573.18 | 0 | −2.31144 | 0 | − | 3.75379i | 0 | 6.99996 | + | 0.0226023i | 0 | −3.65724 | 0 | |||||||||||||||
573.19 | 0 | −2.06233 | 0 | − | 8.76305i | 0 | −1.14613 | + | 6.90553i | 0 | −4.74678 | 0 | |||||||||||||||
573.20 | 0 | −2.06233 | 0 | 8.76305i | 0 | −1.14613 | − | 6.90553i | 0 | −4.74678 | 0 | ||||||||||||||||
See all 56 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.b | odd | 2 | 1 | inner |
41.b | even | 2 | 1 | inner |
287.d | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1148.3.g.a | ✓ | 56 |
7.b | odd | 2 | 1 | inner | 1148.3.g.a | ✓ | 56 |
41.b | even | 2 | 1 | inner | 1148.3.g.a | ✓ | 56 |
287.d | odd | 2 | 1 | inner | 1148.3.g.a | ✓ | 56 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1148.3.g.a | ✓ | 56 | 1.a | even | 1 | 1 | trivial |
1148.3.g.a | ✓ | 56 | 7.b | odd | 2 | 1 | inner |
1148.3.g.a | ✓ | 56 | 41.b | even | 2 | 1 | inner |
1148.3.g.a | ✓ | 56 | 287.d | odd | 2 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1148, [\chi])\).