Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(251,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.bl (of order \(6\), degree \(2\), 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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
251.1 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −2.63140 | + | 0.275220i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.2 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 1.00174 | + | 2.44878i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.3 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −0.474749 | − | 2.60281i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.4 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −1.54699 | + | 2.14635i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.5 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 1.15259 | + | 2.38150i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.6 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −2.13969 | − | 1.55619i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.7 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 2.32919 | − | 1.25494i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.8 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 0.943282 | − | 2.47189i | − | 1.00000i | 0 | − | 1.00000i | ||||||||
251.9 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 2.64304 | − | 0.119814i | 1.00000i | 0 | 1.00000i | ||||||||||
251.10 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 1.22724 | + | 2.34390i | 1.00000i | 0 | 1.00000i | ||||||||||
251.11 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 2.55222 | + | 0.697255i | 1.00000i | 0 | 1.00000i | ||||||||||
251.12 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −2.23931 | − | 1.40907i | 1.00000i | 0 | 1.00000i | ||||||||||
251.13 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | 0.0425252 | − | 2.64541i | 1.00000i | 0 | 1.00000i | ||||||||||
251.14 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −2.17621 | − | 1.50470i | 1.00000i | 0 | 1.00000i | ||||||||||
251.15 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −1.01084 | + | 2.44504i | 1.00000i | 0 | 1.00000i | ||||||||||
251.16 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 0 | −0.672634 | + | 2.55882i | 1.00000i | 0 | 1.00000i | ||||||||||
881.1 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | 0 | −2.63140 | − | 0.275220i | 1.00000i | 0 | 1.00000i | ||||||||||
881.2 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | 0 | 1.00174 | − | 2.44878i | 1.00000i | 0 | 1.00000i | ||||||||||
881.3 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | 0 | −0.474749 | + | 2.60281i | 1.00000i | 0 | 1.00000i | ||||||||||
881.4 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | 0 | −1.54699 | − | 2.14635i | 1.00000i | 0 | 1.00000i | ||||||||||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
63.o | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1890.2.bl.b | 32 | |
3.b | odd | 2 | 1 | 630.2.bl.a | ✓ | 32 | |
7.b | odd | 2 | 1 | 1890.2.bl.a | 32 | ||
9.c | even | 3 | 1 | 630.2.bl.b | yes | 32 | |
9.d | odd | 6 | 1 | 1890.2.bl.a | 32 | ||
21.c | even | 2 | 1 | 630.2.bl.b | yes | 32 | |
63.l | odd | 6 | 1 | 630.2.bl.a | ✓ | 32 | |
63.o | even | 6 | 1 | inner | 1890.2.bl.b | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
630.2.bl.a | ✓ | 32 | 3.b | odd | 2 | 1 | |
630.2.bl.a | ✓ | 32 | 63.l | odd | 6 | 1 | |
630.2.bl.b | yes | 32 | 9.c | even | 3 | 1 | |
630.2.bl.b | yes | 32 | 21.c | even | 2 | 1 | |
1890.2.bl.a | 32 | 7.b | odd | 2 | 1 | ||
1890.2.bl.a | 32 | 9.d | odd | 6 | 1 | ||
1890.2.bl.b | 32 | 1.a | even | 1 | 1 | trivial | |
1890.2.bl.b | 32 | 63.o | even | 6 | 1 | inner |