Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1151,1890)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.1151");
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.t (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: | \(28\) |
Relative dimension: | \(14\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1151.1 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −0.555567 | − | 2.58676i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.2 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −2.36047 | − | 1.19507i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.3 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −0.673503 | + | 2.55859i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.4 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −1.17997 | + | 2.36805i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.5 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | 2.13731 | + | 1.55945i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.6 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | 2.64030 | + | 0.169721i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.7 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −0.142082 | − | 2.64193i | − | 1.00000i | 0 | −0.866025 | − | 0.500000i | |||||||||
1151.8 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −1.57438 | − | 2.12634i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1151.9 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | 2.05946 | + | 1.66090i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1151.10 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | 2.53870 | − | 0.744985i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1151.11 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −2.11261 | − | 1.59276i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1151.12 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −1.82075 | + | 1.91960i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1151.13 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | 1.07313 | + | 2.41835i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1151.14 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | 1.00000 | 0 | −2.02958 | + | 1.69729i | 1.00000i | 0 | 0.866025 | + | 0.500000i | ||||||||||
1601.1 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 1.00000 | 0 | −0.555567 | + | 2.58676i | 1.00000i | 0 | −0.866025 | + | 0.500000i | ||||||||||
1601.2 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 1.00000 | 0 | −2.36047 | + | 1.19507i | 1.00000i | 0 | −0.866025 | + | 0.500000i | ||||||||||
1601.3 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 1.00000 | 0 | −0.673503 | − | 2.55859i | 1.00000i | 0 | −0.866025 | + | 0.500000i | ||||||||||
1601.4 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 1.00000 | 0 | −1.17997 | − | 2.36805i | 1.00000i | 0 | −0.866025 | + | 0.500000i | ||||||||||
1601.5 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 1.00000 | 0 | 2.13731 | − | 1.55945i | 1.00000i | 0 | −0.866025 | + | 0.500000i | ||||||||||
1601.6 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | 1.00000 | 0 | 2.64030 | − | 0.169721i | 1.00000i | 0 | −0.866025 | + | 0.500000i | ||||||||||
See all 28 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
63.s | 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.t.b | 28 | |
3.b | odd | 2 | 1 | 630.2.t.b | ✓ | 28 | |
7.d | odd | 6 | 1 | 1890.2.bk.b | 28 | ||
9.c | even | 3 | 1 | 630.2.bk.b | yes | 28 | |
9.d | odd | 6 | 1 | 1890.2.bk.b | 28 | ||
21.g | even | 6 | 1 | 630.2.bk.b | yes | 28 | |
63.k | odd | 6 | 1 | 630.2.t.b | ✓ | 28 | |
63.s | even | 6 | 1 | inner | 1890.2.t.b | 28 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
630.2.t.b | ✓ | 28 | 3.b | odd | 2 | 1 | |
630.2.t.b | ✓ | 28 | 63.k | odd | 6 | 1 | |
630.2.bk.b | yes | 28 | 9.c | even | 3 | 1 | |
630.2.bk.b | yes | 28 | 21.g | even | 6 | 1 | |
1890.2.t.b | 28 | 1.a | even | 1 | 1 | trivial | |
1890.2.t.b | 28 | 63.s | even | 6 | 1 | inner | |
1890.2.bk.b | 28 | 7.d | odd | 6 | 1 | ||
1890.2.bk.b | 28 | 9.d | odd | 6 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{11}^{28} + 162 T_{11}^{26} + 11301 T_{11}^{24} + 444572 T_{11}^{22} + 10843488 T_{11}^{20} + \cdots + 14197824 \) acting on \(S_{2}^{\mathrm{new}}(1890, [\chi])\).