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: | \(32\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1151.1 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 0.104916 | + | 2.64367i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.2 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 2.63859 | + | 0.194573i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.3 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 1.13965 | − | 2.38772i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.4 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −1.89754 | + | 1.84373i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.5 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −2.46207 | + | 0.968625i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.6 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 0.778946 | − | 2.52849i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.7 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 2.26702 | + | 1.36404i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.8 | −0.866025 | − | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −2.20349 | − | 1.46446i | − | 1.00000i | 0 | 0.866025 | + | 0.500000i | |||||||||
1151.9 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −2.63727 | − | 0.211686i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.10 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 2.60525 | − | 0.461188i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.11 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 1.49710 | + | 2.18144i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.12 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −1.74301 | − | 1.99046i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.13 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −2.64561 | + | 0.0270445i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.14 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | −1.80382 | + | 1.93552i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.15 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 1.16109 | − | 2.37737i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1151.16 | 0.866025 | + | 0.500000i | 0 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 2.20024 | − | 1.46933i | 1.00000i | 0 | −0.866025 | − | 0.500000i | ||||||||||
1601.1 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | −1.00000 | 0 | 0.104916 | − | 2.64367i | 1.00000i | 0 | 0.866025 | − | 0.500000i | ||||||||||
1601.2 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | −1.00000 | 0 | 2.63859 | − | 0.194573i | 1.00000i | 0 | 0.866025 | − | 0.500000i | ||||||||||
1601.3 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | −1.00000 | 0 | 1.13965 | + | 2.38772i | 1.00000i | 0 | 0.866025 | − | 0.500000i | ||||||||||
1601.4 | −0.866025 | + | 0.500000i | 0 | 0.500000 | − | 0.866025i | −1.00000 | 0 | −1.89754 | − | 1.84373i | 1.00000i | 0 | 0.866025 | − | 0.500000i | ||||||||||
See all 32 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.c | 32 | |
3.b | odd | 2 | 1 | 630.2.t.c | ✓ | 32 | |
7.d | odd | 6 | 1 | 1890.2.bk.c | 32 | ||
9.c | even | 3 | 1 | 630.2.bk.c | yes | 32 | |
9.d | odd | 6 | 1 | 1890.2.bk.c | 32 | ||
21.g | even | 6 | 1 | 630.2.bk.c | yes | 32 | |
63.k | odd | 6 | 1 | 630.2.t.c | ✓ | 32 | |
63.s | even | 6 | 1 | inner | 1890.2.t.c | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
630.2.t.c | ✓ | 32 | 3.b | odd | 2 | 1 | |
630.2.t.c | ✓ | 32 | 63.k | odd | 6 | 1 | |
630.2.bk.c | yes | 32 | 9.c | even | 3 | 1 | |
630.2.bk.c | yes | 32 | 21.g | even | 6 | 1 | |
1890.2.t.c | 32 | 1.a | even | 1 | 1 | trivial | |
1890.2.t.c | 32 | 63.s | even | 6 | 1 | inner | |
1890.2.bk.c | 32 | 7.d | odd | 6 | 1 | ||
1890.2.bk.c | 32 | 9.d | odd | 6 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{11}^{32} + 186 T_{11}^{30} + 15033 T_{11}^{28} + 694868 T_{11}^{26} + 20357652 T_{11}^{24} + 396304476 T_{11}^{22} + 5234074446 T_{11}^{20} + 47134336614 T_{11}^{18} + 287650283280 T_{11}^{16} + \cdots + 7925984784 \)
acting on \(S_{2}^{\mathrm{new}}(1890, [\chi])\).