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 | −2.66525 | 0.180914 | 5.10356 | 1.00000 | −0.482180 | −2.30037 | −8.27176 | −2.96727 | −2.66525 | ||||||||||||||||||
1.2 | −2.40320 | 1.20051 | 3.77538 | 1.00000 | −2.88508 | −1.77185 | −4.26659 | −1.55876 | −2.40320 | ||||||||||||||||||
1.3 | −2.39029 | −2.40790 | 3.71350 | 1.00000 | 5.75558 | 4.16969 | −4.09576 | 2.79797 | −2.39029 | ||||||||||||||||||
1.4 | −2.31945 | −2.05009 | 3.37984 | 1.00000 | 4.75509 | 0.529758 | −3.20047 | 1.20289 | −2.31945 | ||||||||||||||||||
1.5 | −2.29064 | 1.47549 | 3.24701 | 1.00000 | −3.37981 | 2.13493 | −2.85645 | −0.822934 | −2.29064 | ||||||||||||||||||
1.6 | −1.85242 | 0.130041 | 1.43148 | 1.00000 | −0.240891 | 2.44217 | 1.05315 | −2.98309 | −1.85242 | ||||||||||||||||||
1.7 | −1.71589 | −3.02116 | 0.944266 | 1.00000 | 5.18397 | −0.410823 | 1.81152 | 6.12740 | −1.71589 | ||||||||||||||||||
1.8 | −1.63901 | 0.960813 | 0.686340 | 1.00000 | −1.57478 | 4.58027 | 2.15310 | −2.07684 | −1.63901 | ||||||||||||||||||
1.9 | −1.62869 | 2.31397 | 0.652617 | 1.00000 | −3.76873 | −4.05639 | 2.19446 | 2.35446 | −1.62869 | ||||||||||||||||||
1.10 | −1.59880 | −0.663250 | 0.556157 | 1.00000 | 1.06040 | −3.10735 | 2.30841 | −2.56010 | −1.59880 | ||||||||||||||||||
1.11 | −1.59058 | 2.74131 | 0.529934 | 1.00000 | −4.36027 | 0.195561 | 2.33825 | 4.51480 | −1.59058 | ||||||||||||||||||
1.12 | −1.02277 | −0.691517 | −0.953933 | 1.00000 | 0.707265 | 1.61582 | 3.02121 | −2.52180 | −1.02277 | ||||||||||||||||||
1.13 | −0.861525 | −2.77636 | −1.25777 | 1.00000 | 2.39191 | 0.623554 | 2.80665 | 4.70820 | −0.861525 | ||||||||||||||||||
1.14 | −0.644629 | 1.56810 | −1.58445 | 1.00000 | −1.01085 | 2.57685 | 2.31064 | −0.541047 | −0.644629 | ||||||||||||||||||
1.15 | −0.619688 | −2.94210 | −1.61599 | 1.00000 | 1.82319 | −1.69113 | 2.24078 | 5.65598 | −0.619688 | ||||||||||||||||||
1.16 | −0.381657 | −0.970824 | −1.85434 | 1.00000 | 0.370521 | −3.53323 | 1.47103 | −2.05750 | −0.381657 | ||||||||||||||||||
1.17 | −0.163606 | −0.433822 | −1.97323 | 1.00000 | 0.0709760 | 2.35725 | 0.650046 | −2.81180 | −0.163606 | ||||||||||||||||||
1.18 | −0.134450 | −0.934655 | −1.98192 | 1.00000 | 0.125664 | −1.20552 | 0.535370 | −2.12642 | −0.134450 | ||||||||||||||||||
1.19 | −0.0473223 | 3.03750 | −1.99776 | 1.00000 | −0.143741 | −2.32686 | 0.189183 | 6.22638 | −0.0473223 | ||||||||||||||||||
1.20 | 0.111835 | 1.47233 | −1.98749 | 1.00000 | 0.164659 | −0.779752 | −0.445943 | −0.832238 | 0.111835 | ||||||||||||||||||
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.b | ✓ | 36 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6035.2.a.b | ✓ | 36 | 1.a | even | 1 | 1 | trivial |