Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(323,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.323");
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.m (of order \(4\), degree \(2\), 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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
323.1 | −0.707107 | − | 0.707107i | 0 | 1.00000i | 1.38028 | + | 1.75922i | 0 | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 0 | 0.267951 | − | 2.21996i | ||||||||
323.2 | −0.707107 | − | 0.707107i | 0 | 1.00000i | −2.09650 | − | 0.777612i | 0 | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 0 | 0.932595 | + | 2.03231i | ||||||||
323.3 | −0.707107 | − | 0.707107i | 0 | 1.00000i | −1.10768 | + | 1.94243i | 0 | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 0 | 2.15676 | − | 0.590258i | ||||||||
323.4 | −0.707107 | − | 0.707107i | 0 | 1.00000i | 1.45741 | + | 1.69586i | 0 | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 0 | 0.168613 | − | 2.22970i | ||||||||
323.5 | −0.707107 | − | 0.707107i | 0 | 1.00000i | 1.92333 | − | 1.14052i | 0 | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 0 | −2.16647 | − | 0.553531i | ||||||||
323.6 | −0.707107 | − | 0.707107i | 0 | 1.00000i | 0.857378 | − | 2.06516i | 0 | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | 0 | −2.06655 | + | 0.854034i | ||||||||
323.7 | 0.707107 | + | 0.707107i | 0 | 1.00000i | 2.19971 | − | 0.401567i | 0 | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 0 | 1.83938 | + | 1.27148i | ||||||||
323.8 | 0.707107 | + | 0.707107i | 0 | 1.00000i | 2.02160 | − | 0.955573i | 0 | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 0 | 2.10518 | + | 0.753797i | ||||||||
323.9 | 0.707107 | + | 0.707107i | 0 | 1.00000i | −1.98740 | + | 1.02482i | 0 | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 0 | −2.12996 | − | 0.680649i | ||||||||
323.10 | 0.707107 | + | 0.707107i | 0 | 1.00000i | −0.283889 | + | 2.21797i | 0 | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 0 | −1.76908 | + | 1.36760i | ||||||||
323.11 | 0.707107 | + | 0.707107i | 0 | 1.00000i | −1.94482 | − | 1.10348i | 0 | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 0 | −0.594917 | − | 2.15548i | ||||||||
323.12 | 0.707107 | + | 0.707107i | 0 | 1.00000i | −0.419422 | − | 2.19638i | 0 | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | 0 | 1.25650 | − | 1.84965i | ||||||||
1457.1 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | 1.38028 | − | 1.75922i | 0 | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0 | 0.267951 | + | 2.21996i | |||||||
1457.2 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | −2.09650 | + | 0.777612i | 0 | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0 | 0.932595 | − | 2.03231i | |||||||
1457.3 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | −1.10768 | − | 1.94243i | 0 | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0 | 2.15676 | + | 0.590258i | |||||||
1457.4 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | 1.45741 | − | 1.69586i | 0 | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0 | 0.168613 | + | 2.22970i | |||||||
1457.5 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | 1.92333 | + | 1.14052i | 0 | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0 | −2.16647 | + | 0.553531i | |||||||
1457.6 | −0.707107 | + | 0.707107i | 0 | − | 1.00000i | 0.857378 | + | 2.06516i | 0 | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | 0 | −2.06655 | − | 0.854034i | |||||||
1457.7 | 0.707107 | − | 0.707107i | 0 | − | 1.00000i | 2.19971 | + | 0.401567i | 0 | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0 | 1.83938 | − | 1.27148i | |||||||
1457.8 | 0.707107 | − | 0.707107i | 0 | − | 1.00000i | 2.02160 | + | 0.955573i | 0 | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | 0 | 2.10518 | − | 0.753797i | |||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
15.e | even | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1890.2.m.c | yes | 24 |
3.b | odd | 2 | 1 | 1890.2.m.b | ✓ | 24 | |
5.c | odd | 4 | 1 | 1890.2.m.b | ✓ | 24 | |
15.e | even | 4 | 1 | inner | 1890.2.m.c | yes | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1890.2.m.b | ✓ | 24 | 3.b | odd | 2 | 1 | |
1890.2.m.b | ✓ | 24 | 5.c | odd | 4 | 1 | |
1890.2.m.c | yes | 24 | 1.a | even | 1 | 1 | trivial |
1890.2.m.c | yes | 24 | 15.e | even | 4 | 1 | inner |