Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [633,6,Mod(1,633)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(633, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("633.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 633 = 3 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 633.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: | \(101.522957942\) |
Analytic rank: | \(0\) |
Dimension: | \(43\) |
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 | −10.4485 | −9.00000 | 77.1701 | 32.3344 | 94.0361 | 106.301 | −471.958 | 81.0000 | −337.844 | ||||||||||||||||||
1.2 | −10.3217 | −9.00000 | 74.5376 | 22.9849 | 92.8954 | 124.903 | −439.061 | 81.0000 | −237.243 | ||||||||||||||||||
1.3 | −9.95524 | −9.00000 | 67.1069 | −51.5368 | 89.5972 | −153.923 | −349.497 | 81.0000 | 513.061 | ||||||||||||||||||
1.4 | −9.63790 | −9.00000 | 60.8892 | 22.2688 | 86.7411 | −180.808 | −278.431 | 81.0000 | −214.625 | ||||||||||||||||||
1.5 | −8.70572 | −9.00000 | 43.7895 | 93.3937 | 78.3515 | 196.820 | −102.636 | 81.0000 | −813.059 | ||||||||||||||||||
1.6 | −8.60921 | −9.00000 | 42.1186 | −87.1953 | 77.4829 | 95.7003 | −87.1129 | 81.0000 | 750.683 | ||||||||||||||||||
1.7 | −8.40613 | −9.00000 | 38.6630 | −14.5903 | 75.6552 | −42.4616 | −56.0100 | 81.0000 | 122.648 | ||||||||||||||||||
1.8 | −8.37304 | −9.00000 | 38.1079 | 8.08613 | 75.3574 | 183.646 | −51.1415 | 81.0000 | −67.7055 | ||||||||||||||||||
1.9 | −7.93873 | −9.00000 | 31.0235 | 76.9177 | 71.4486 | 9.33725 | 7.75222 | 81.0000 | −610.629 | ||||||||||||||||||
1.10 | −6.27027 | −9.00000 | 7.31630 | −72.9967 | 56.4324 | −132.363 | 154.773 | 81.0000 | 457.709 | ||||||||||||||||||
1.11 | −5.12190 | −9.00000 | −5.76617 | 82.2225 | 46.0971 | 121.113 | 193.434 | 81.0000 | −421.135 | ||||||||||||||||||
1.12 | −4.79000 | −9.00000 | −9.05586 | −94.8244 | 43.1100 | −26.7586 | 196.658 | 81.0000 | 454.209 | ||||||||||||||||||
1.13 | −4.69088 | −9.00000 | −9.99560 | 97.6143 | 42.2180 | −138.970 | 196.997 | 81.0000 | −457.897 | ||||||||||||||||||
1.14 | −4.50212 | −9.00000 | −11.7309 | −35.2568 | 40.5191 | −74.8838 | 196.882 | 81.0000 | 158.730 | ||||||||||||||||||
1.15 | −3.78564 | −9.00000 | −17.6689 | −94.6688 | 34.0707 | 65.0006 | 188.029 | 81.0000 | 358.382 | ||||||||||||||||||
1.16 | −3.18591 | −9.00000 | −21.8500 | 29.8535 | 28.6732 | −163.113 | 171.561 | 81.0000 | −95.1108 | ||||||||||||||||||
1.17 | −2.08669 | −9.00000 | −27.6457 | 60.2817 | 18.7802 | −112.841 | 124.462 | 81.0000 | −125.789 | ||||||||||||||||||
1.18 | −1.34138 | −9.00000 | −30.2007 | −20.1300 | 12.0724 | −159.138 | 83.4346 | 81.0000 | 27.0020 | ||||||||||||||||||
1.19 | −1.05971 | −9.00000 | −30.8770 | −9.18692 | 9.53741 | 152.911 | 66.6315 | 81.0000 | 9.73549 | ||||||||||||||||||
1.20 | −0.834509 | −9.00000 | −31.3036 | −46.8133 | 7.51058 | 118.944 | 52.8274 | 81.0000 | 39.0662 | ||||||||||||||||||
See all 43 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(211\) | \(-1\) |
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 | 633.6.a.b | ✓ | 43 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
633.6.a.b | ✓ | 43 | 1.a | even | 1 | 1 | trivial |