Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [798,4,Mod(265,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("798.265");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.e (of order \(2\), degree \(1\), 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: | \(47.0835241846\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
265.1 | − | 2.00000i | −3.00000 | −4.00000 | − | 20.6257i | 6.00000i | −17.3451 | − | 6.49217i | 8.00000i | 9.00000 | −41.2513 | ||||||||||||||
265.2 | − | 2.00000i | −3.00000 | −4.00000 | − | 17.7805i | 6.00000i | 18.3340 | − | 2.61970i | 8.00000i | 9.00000 | −35.5610 | ||||||||||||||
265.3 | − | 2.00000i | −3.00000 | −4.00000 | − | 14.0192i | 6.00000i | −18.5089 | − | 0.647553i | 8.00000i | 9.00000 | −28.0385 | ||||||||||||||
265.4 | − | 2.00000i | −3.00000 | −4.00000 | − | 13.9658i | 6.00000i | −2.20869 | − | 18.3881i | 8.00000i | 9.00000 | −27.9317 | ||||||||||||||
265.5 | − | 2.00000i | −3.00000 | −4.00000 | − | 13.3323i | 6.00000i | 4.59040 | + | 17.9424i | 8.00000i | 9.00000 | −26.6647 | ||||||||||||||
265.6 | − | 2.00000i | −3.00000 | −4.00000 | − | 11.4338i | 6.00000i | 12.7533 | − | 13.4296i | 8.00000i | 9.00000 | −22.8677 | ||||||||||||||
265.7 | − | 2.00000i | −3.00000 | −4.00000 | − | 9.83057i | 6.00000i | −9.74124 | + | 15.7515i | 8.00000i | 9.00000 | −19.6611 | ||||||||||||||
265.8 | − | 2.00000i | −3.00000 | −4.00000 | − | 8.60585i | 6.00000i | 8.72974 | + | 16.3338i | 8.00000i | 9.00000 | −17.2117 | ||||||||||||||
265.9 | − | 2.00000i | −3.00000 | −4.00000 | − | 3.30270i | 6.00000i | −0.332747 | − | 18.5173i | 8.00000i | 9.00000 | −6.60540 | ||||||||||||||
265.10 | − | 2.00000i | −3.00000 | −4.00000 | 3.24183i | 6.00000i | −15.2716 | − | 10.4775i | 8.00000i | 9.00000 | 6.48366 | |||||||||||||||
265.11 | − | 2.00000i | −3.00000 | −4.00000 | 3.45330i | 6.00000i | 14.3222 | + | 11.7420i | 8.00000i | 9.00000 | 6.90659 | |||||||||||||||
265.12 | − | 2.00000i | −3.00000 | −4.00000 | 3.49808i | 6.00000i | −15.4528 | + | 10.2084i | 8.00000i | 9.00000 | 6.99615 | |||||||||||||||
265.13 | − | 2.00000i | −3.00000 | −4.00000 | 7.72726i | 6.00000i | 10.3686 | − | 15.3458i | 8.00000i | 9.00000 | 15.4545 | |||||||||||||||
265.14 | − | 2.00000i | −3.00000 | −4.00000 | 8.71306i | 6.00000i | 16.3570 | − | 8.68615i | 8.00000i | 9.00000 | 17.4261 | |||||||||||||||
265.15 | − | 2.00000i | −3.00000 | −4.00000 | 8.72794i | 6.00000i | −3.02218 | + | 18.2720i | 8.00000i | 9.00000 | 17.4559 | |||||||||||||||
265.16 | − | 2.00000i | −3.00000 | −4.00000 | 9.44152i | 6.00000i | 18.5105 | − | 0.601895i | 8.00000i | 9.00000 | 18.8830 | |||||||||||||||
265.17 | − | 2.00000i | −3.00000 | −4.00000 | 14.5846i | 6.00000i | −9.84423 | − | 15.6873i | 8.00000i | 9.00000 | 29.1693 | |||||||||||||||
265.18 | − | 2.00000i | −3.00000 | −4.00000 | 14.5913i | 6.00000i | −13.0767 | + | 13.1149i | 8.00000i | 9.00000 | 29.1826 | |||||||||||||||
265.19 | − | 2.00000i | −3.00000 | −4.00000 | 18.2708i | 6.00000i | −16.6167 | − | 8.17834i | 8.00000i | 9.00000 | 36.5417 | |||||||||||||||
265.20 | − | 2.00000i | −3.00000 | −4.00000 | 18.6467i | 6.00000i | 12.4552 | + | 13.7065i | 8.00000i | 9.00000 | 37.2934 | |||||||||||||||
See all 40 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
133.c | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 798.4.e.a | ✓ | 40 |
7.b | odd | 2 | 1 | 798.4.e.b | yes | 40 | |
19.b | odd | 2 | 1 | 798.4.e.b | yes | 40 | |
133.c | even | 2 | 1 | inner | 798.4.e.a | ✓ | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
798.4.e.a | ✓ | 40 | 1.a | even | 1 | 1 | trivial |
798.4.e.a | ✓ | 40 | 133.c | even | 2 | 1 | inner |
798.4.e.b | yes | 40 | 7.b | odd | 2 | 1 | |
798.4.e.b | yes | 40 | 19.b | odd | 2 | 1 |