Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(719,1890)]
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([5, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.719");
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.bi (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: | \(48\) |
Relative dimension: | \(24\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
719.1 | −1.00000 | 0 | 1.00000 | −2.22760 | − | 0.194363i | 0 | −2.20085 | + | 1.46842i | −1.00000 | 0 | 2.22760 | + | 0.194363i | ||||||||||||
719.2 | −1.00000 | 0 | 1.00000 | −2.20530 | + | 0.369687i | 0 | 2.33660 | − | 1.24108i | −1.00000 | 0 | 2.20530 | − | 0.369687i | ||||||||||||
719.3 | −1.00000 | 0 | 1.00000 | −2.07140 | − | 0.842204i | 0 | −1.57200 | − | 2.12810i | −1.00000 | 0 | 2.07140 | + | 0.842204i | ||||||||||||
719.4 | −1.00000 | 0 | 1.00000 | −1.98394 | + | 1.03150i | 0 | 0.994947 | + | 2.45155i | −1.00000 | 0 | 1.98394 | − | 1.03150i | ||||||||||||
719.5 | −1.00000 | 0 | 1.00000 | −1.67933 | + | 1.47644i | 0 | −2.41546 | − | 1.07960i | −1.00000 | 0 | 1.67933 | − | 1.47644i | ||||||||||||
719.6 | −1.00000 | 0 | 1.00000 | −1.41134 | − | 1.73440i | 0 | 2.55753 | + | 0.677517i | −1.00000 | 0 | 1.41134 | + | 1.73440i | ||||||||||||
719.7 | −1.00000 | 0 | 1.00000 | −1.24107 | − | 1.86004i | 0 | 2.20215 | − | 1.46647i | −1.00000 | 0 | 1.24107 | + | 1.86004i | ||||||||||||
719.8 | −1.00000 | 0 | 1.00000 | −1.22943 | + | 1.86775i | 0 | −0.691773 | + | 2.55371i | −1.00000 | 0 | 1.22943 | − | 1.86775i | ||||||||||||
719.9 | −1.00000 | 0 | 1.00000 | −0.719036 | − | 2.11731i | 0 | −1.31170 | + | 2.29771i | −1.00000 | 0 | 0.719036 | + | 2.11731i | ||||||||||||
719.10 | −1.00000 | 0 | 1.00000 | −0.543458 | + | 2.16902i | 0 | −1.39638 | − | 2.24725i | −1.00000 | 0 | 0.543458 | − | 2.16902i | ||||||||||||
719.11 | −1.00000 | 0 | 1.00000 | −0.325622 | − | 2.21223i | 0 | −1.75469 | − | 1.98017i | −1.00000 | 0 | 0.325622 | + | 2.21223i | ||||||||||||
719.12 | −1.00000 | 0 | 1.00000 | −0.307273 | + | 2.21486i | 0 | −0.431605 | − | 2.61031i | −1.00000 | 0 | 0.307273 | − | 2.21486i | ||||||||||||
719.13 | −1.00000 | 0 | 1.00000 | −0.0611015 | − | 2.23523i | 0 | 1.83478 | + | 1.90619i | −1.00000 | 0 | 0.0611015 | + | 2.23523i | ||||||||||||
719.14 | −1.00000 | 0 | 1.00000 | 0.255938 | + | 2.22137i | 0 | 2.61687 | + | 0.389830i | −1.00000 | 0 | −0.255938 | − | 2.22137i | ||||||||||||
719.15 | −1.00000 | 0 | 1.00000 | 0.381768 | + | 2.20324i | 0 | 2.63972 | − | 0.178501i | −1.00000 | 0 | −0.381768 | − | 2.20324i | ||||||||||||
719.16 | −1.00000 | 0 | 1.00000 | 0.834189 | + | 2.07464i | 0 | −1.94702 | + | 1.79140i | −1.00000 | 0 | −0.834189 | − | 2.07464i | ||||||||||||
719.17 | −1.00000 | 0 | 1.00000 | 0.930691 | − | 2.03318i | 0 | −2.58635 | + | 0.557485i | −1.00000 | 0 | −0.930691 | + | 2.03318i | ||||||||||||
719.18 | −1.00000 | 0 | 1.00000 | 1.55089 | − | 1.61082i | 0 | −0.405354 | − | 2.61451i | −1.00000 | 0 | −1.55089 | + | 1.61082i | ||||||||||||
719.19 | −1.00000 | 0 | 1.00000 | 1.71175 | − | 1.43872i | 0 | 2.20678 | + | 1.45950i | −1.00000 | 0 | −1.71175 | + | 1.43872i | ||||||||||||
719.20 | −1.00000 | 0 | 1.00000 | 1.93822 | − | 1.11504i | 0 | 1.80444 | − | 1.93494i | −1.00000 | 0 | −1.93822 | + | 1.11504i | ||||||||||||
See all 48 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
315.bq | 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.bi.a | 48 | |
3.b | odd | 2 | 1 | 630.2.bi.b | yes | 48 | |
5.b | even | 2 | 1 | 1890.2.bi.b | 48 | ||
7.d | odd | 6 | 1 | 1890.2.r.b | 48 | ||
9.c | even | 3 | 1 | 630.2.r.b | yes | 48 | |
9.d | odd | 6 | 1 | 1890.2.r.a | 48 | ||
15.d | odd | 2 | 1 | 630.2.bi.a | yes | 48 | |
21.g | even | 6 | 1 | 630.2.r.a | ✓ | 48 | |
35.i | odd | 6 | 1 | 1890.2.r.a | 48 | ||
45.h | odd | 6 | 1 | 1890.2.r.b | 48 | ||
45.j | even | 6 | 1 | 630.2.r.a | ✓ | 48 | |
63.i | even | 6 | 1 | 1890.2.bi.b | 48 | ||
63.t | odd | 6 | 1 | 630.2.bi.a | yes | 48 | |
105.p | even | 6 | 1 | 630.2.r.b | yes | 48 | |
315.q | odd | 6 | 1 | 630.2.bi.b | yes | 48 | |
315.bq | even | 6 | 1 | inner | 1890.2.bi.a | 48 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
630.2.r.a | ✓ | 48 | 21.g | even | 6 | 1 | |
630.2.r.a | ✓ | 48 | 45.j | even | 6 | 1 | |
630.2.r.b | yes | 48 | 9.c | even | 3 | 1 | |
630.2.r.b | yes | 48 | 105.p | even | 6 | 1 | |
630.2.bi.a | yes | 48 | 15.d | odd | 2 | 1 | |
630.2.bi.a | yes | 48 | 63.t | odd | 6 | 1 | |
630.2.bi.b | yes | 48 | 3.b | odd | 2 | 1 | |
630.2.bi.b | yes | 48 | 315.q | odd | 6 | 1 | |
1890.2.r.a | 48 | 9.d | odd | 6 | 1 | ||
1890.2.r.a | 48 | 35.i | odd | 6 | 1 | ||
1890.2.r.b | 48 | 7.d | odd | 6 | 1 | ||
1890.2.r.b | 48 | 45.h | odd | 6 | 1 | ||
1890.2.bi.a | 48 | 1.a | even | 1 | 1 | trivial | |
1890.2.bi.a | 48 | 315.bq | even | 6 | 1 | inner | |
1890.2.bi.b | 48 | 5.b | even | 2 | 1 | ||
1890.2.bi.b | 48 | 63.i | even | 6 | 1 |