Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.a (trivial) |
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: | yes |
Analytic conductor: | \(48.1897176198\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −2.62226 | −1.54085 | 4.87626 | 1.00000 | 4.04052 | 0.0125838 | −7.54231 | −0.625776 | −2.62226 | ||||||||||||||||||
1.2 | −2.61440 | 2.49037 | 4.83510 | 1.00000 | −6.51084 | 2.00109 | −7.41211 | 3.20197 | −2.61440 | ||||||||||||||||||
1.3 | −2.37331 | 2.40096 | 3.63259 | 1.00000 | −5.69821 | −2.59145 | −3.87465 | 2.76459 | −2.37331 | ||||||||||||||||||
1.4 | −2.27701 | 0.848689 | 3.18476 | 1.00000 | −1.93247 | 1.85809 | −2.69770 | −2.27973 | −2.27701 | ||||||||||||||||||
1.5 | −2.15542 | −0.292006 | 2.64584 | 1.00000 | 0.629396 | −5.08250 | −1.39207 | −2.91473 | −2.15542 | ||||||||||||||||||
1.6 | −2.13074 | −1.60683 | 2.54004 | 1.00000 | 3.42373 | 2.82688 | −1.15069 | −0.418101 | −2.13074 | ||||||||||||||||||
1.7 | −2.04946 | −2.65729 | 2.20029 | 1.00000 | 5.44602 | −0.551924 | −0.410497 | 4.06121 | −2.04946 | ||||||||||||||||||
1.8 | −1.90835 | −2.27887 | 1.64180 | 1.00000 | 4.34888 | −0.428939 | 0.683573 | 2.19324 | −1.90835 | ||||||||||||||||||
1.9 | −1.70160 | 0.687277 | 0.895431 | 1.00000 | −1.16947 | −0.626542 | 1.87953 | −2.52765 | −1.70160 | ||||||||||||||||||
1.10 | −1.14290 | −1.19489 | −0.693776 | 1.00000 | 1.36564 | −1.41810 | 3.07872 | −1.57223 | −1.14290 | ||||||||||||||||||
1.11 | −1.12696 | 2.34856 | −0.729961 | 1.00000 | −2.64673 | −2.68480 | 3.07656 | 2.51573 | −1.12696 | ||||||||||||||||||
1.12 | −1.12140 | 0.383871 | −0.742456 | 1.00000 | −0.430474 | 1.34550 | 3.07540 | −2.85264 | −1.12140 | ||||||||||||||||||
1.13 | −1.03393 | 2.68090 | −0.930989 | 1.00000 | −2.77186 | 1.41622 | 3.03044 | 4.18720 | −1.03393 | ||||||||||||||||||
1.14 | −0.904707 | −2.66665 | −1.18150 | 1.00000 | 2.41254 | 3.83492 | 2.87833 | 4.11101 | −0.904707 | ||||||||||||||||||
1.15 | −0.890323 | −0.682987 | −1.20732 | 1.00000 | 0.608079 | 2.96744 | 2.85556 | −2.53353 | −0.890323 | ||||||||||||||||||
1.16 | −0.599472 | −1.15414 | −1.64063 | 1.00000 | 0.691877 | −3.77052 | 2.18246 | −1.66795 | −0.599472 | ||||||||||||||||||
1.17 | −0.256013 | 0.196473 | −1.93446 | 1.00000 | −0.0502997 | 2.99337 | 1.00727 | −2.96140 | −0.256013 | ||||||||||||||||||
1.18 | −0.174528 | 1.77073 | −1.96954 | 1.00000 | −0.309043 | −0.0296109 | 0.692797 | 0.135502 | −0.174528 | ||||||||||||||||||
1.19 | 0.0925953 | 0.181897 | −1.99143 | 1.00000 | 0.0168428 | −0.294707 | −0.369587 | −2.96691 | 0.0925953 | ||||||||||||||||||
1.20 | 0.139816 | −2.98888 | −1.98045 | 1.00000 | −0.417894 | 2.58191 | −0.556532 | 5.93339 | 0.139816 | ||||||||||||||||||
See all 36 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(-1\) |
\(17\) | \(-1\) |
\(71\) | \(1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 6035.2.a.a | ✓ | 36 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6035.2.a.a | ✓ | 36 | 1.a | even | 1 | 1 | trivial |