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: | \(44\) |
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 | −2.70129 | 0.655532 | 5.29696 | −1.00000 | −1.77078 | −0.0621637 | −8.90605 | −2.57028 | 2.70129 | ||||||||||||||||||
1.2 | −2.64749 | −3.20996 | 5.00919 | −1.00000 | 8.49832 | 0.615525 | −7.96680 | 7.30382 | 2.64749 | ||||||||||||||||||
1.3 | −2.64188 | −2.73778 | 4.97955 | −1.00000 | 7.23290 | −2.76767 | −7.87163 | 4.49544 | 2.64188 | ||||||||||||||||||
1.4 | −2.46938 | 3.07673 | 4.09785 | −1.00000 | −7.59763 | −1.91212 | −5.18041 | 6.46627 | 2.46938 | ||||||||||||||||||
1.5 | −2.34625 | 1.66109 | 3.50491 | −1.00000 | −3.89733 | −1.01758 | −3.53091 | −0.240793 | 2.34625 | ||||||||||||||||||
1.6 | −2.23368 | −1.23586 | 2.98933 | −1.00000 | 2.76051 | 4.57828 | −2.20985 | −1.47266 | 2.23368 | ||||||||||||||||||
1.7 | −2.19317 | −2.27745 | 2.80998 | −1.00000 | 4.99483 | 0.0320712 | −1.77641 | 2.18678 | 2.19317 | ||||||||||||||||||
1.8 | −2.08101 | −0.567125 | 2.33060 | −1.00000 | 1.18019 | 0.262540 | −0.687984 | −2.67837 | 2.08101 | ||||||||||||||||||
1.9 | −1.95978 | 3.22688 | 1.84076 | −1.00000 | −6.32398 | −0.0576058 | 0.312084 | 7.41274 | 1.95978 | ||||||||||||||||||
1.10 | −1.90817 | 0.344959 | 1.64110 | −1.00000 | −0.658240 | −4.54756 | 0.684835 | −2.88100 | 1.90817 | ||||||||||||||||||
1.11 | −1.80391 | −0.126904 | 1.25409 | −1.00000 | 0.228923 | 3.02972 | 1.34555 | −2.98390 | 1.80391 | ||||||||||||||||||
1.12 | −1.46857 | −1.96529 | 0.156709 | −1.00000 | 2.88617 | 0.231014 | 2.70701 | 0.862355 | 1.46857 | ||||||||||||||||||
1.13 | −1.27664 | −0.663809 | −0.370186 | −1.00000 | 0.847446 | −4.75161 | 3.02588 | −2.55936 | 1.27664 | ||||||||||||||||||
1.14 | −1.22108 | 2.84646 | −0.508955 | −1.00000 | −3.47576 | 3.55048 | 3.06364 | 5.10232 | 1.22108 | ||||||||||||||||||
1.15 | −1.11770 | 1.99244 | −0.750750 | −1.00000 | −2.22695 | 1.05748 | 3.07451 | 0.969828 | 1.11770 | ||||||||||||||||||
1.16 | −1.11582 | 1.42777 | −0.754948 | −1.00000 | −1.59313 | 2.73962 | 3.07402 | −0.961481 | 1.11582 | ||||||||||||||||||
1.17 | −0.992710 | 0.0314056 | −1.01453 | −1.00000 | −0.0311766 | −2.95414 | 2.99255 | −2.99901 | 0.992710 | ||||||||||||||||||
1.18 | −0.913846 | −2.84047 | −1.16489 | −1.00000 | 2.59575 | −2.85023 | 2.89222 | 5.06825 | 0.913846 | ||||||||||||||||||
1.19 | −0.852540 | −3.38177 | −1.27318 | −1.00000 | 2.88309 | 2.95179 | 2.79051 | 8.43634 | 0.852540 | ||||||||||||||||||
1.20 | −0.468055 | −1.11250 | −1.78092 | −1.00000 | 0.520709 | 2.43042 | 1.76968 | −1.76235 | 0.468055 | ||||||||||||||||||
See all 44 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.c | ✓ | 44 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6035.2.a.c | ✓ | 44 | 1.a | even | 1 | 1 | trivial |