Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,6,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(157.657294876\) |
Analytic rank: | \(1\) |
Dimension: | \(191\) |
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 | −11.1976 | −23.7621 | 93.3852 | 76.4799 | 266.078 | −19.5877 | −687.365 | 321.638 | −856.388 | ||||||||||||||||||
1.2 | −11.1262 | 29.5188 | 91.7918 | 67.1507 | −328.432 | −250.979 | −665.254 | 628.360 | −747.131 | ||||||||||||||||||
1.3 | −10.9287 | 4.75838 | 87.4366 | −74.3663 | −52.0029 | −185.895 | −605.851 | −220.358 | 812.728 | ||||||||||||||||||
1.4 | −10.8272 | 14.3547 | 85.2276 | −26.4676 | −155.420 | 140.784 | −576.304 | −36.9436 | 286.569 | ||||||||||||||||||
1.5 | −10.8057 | 19.0440 | 84.7636 | −41.1837 | −205.784 | −3.45765 | −570.149 | 119.674 | 445.020 | ||||||||||||||||||
1.6 | −10.7746 | −26.7262 | 84.0930 | −46.3632 | 287.965 | −164.750 | −561.284 | 471.287 | 499.547 | ||||||||||||||||||
1.7 | −10.6536 | −21.7329 | 81.4987 | −24.1347 | 231.533 | 102.660 | −527.338 | 229.319 | 257.121 | ||||||||||||||||||
1.8 | −10.6191 | 17.1432 | 80.7650 | 60.4272 | −182.045 | 43.6018 | −517.839 | 50.8902 | −641.681 | ||||||||||||||||||
1.9 | −10.4383 | −14.1728 | 76.9585 | 25.9677 | 147.941 | 174.030 | −469.291 | −42.1308 | −271.059 | ||||||||||||||||||
1.10 | −10.4121 | −2.05023 | 76.4119 | 54.9016 | 21.3472 | 184.115 | −462.422 | −238.797 | −571.641 | ||||||||||||||||||
1.11 | −10.1648 | 24.7155 | 71.3234 | −57.1368 | −251.229 | −211.752 | −399.716 | 367.858 | 580.785 | ||||||||||||||||||
1.12 | −10.0336 | −29.0942 | 68.6734 | −75.3888 | 291.920 | 17.3499 | −367.966 | 603.471 | 756.422 | ||||||||||||||||||
1.13 | −9.88271 | −13.0845 | 65.6680 | −13.4569 | 129.310 | −107.789 | −332.731 | −71.7966 | 132.990 | ||||||||||||||||||
1.14 | −9.83897 | −20.7623 | 64.8053 | 50.1722 | 204.279 | 3.16220 | −322.770 | 188.071 | −493.643 | ||||||||||||||||||
1.15 | −9.80318 | 16.6427 | 64.1023 | 2.99274 | −163.152 | −200.824 | −314.705 | 33.9806 | −29.3383 | ||||||||||||||||||
1.16 | −9.78124 | 27.6828 | 63.6727 | 21.4120 | −270.772 | 51.6520 | −309.799 | 523.335 | −209.436 | ||||||||||||||||||
1.17 | −9.77505 | 10.8192 | 63.5517 | −59.8667 | −105.759 | −143.755 | −308.419 | −125.944 | 585.200 | ||||||||||||||||||
1.18 | −9.77050 | −4.83034 | 63.4627 | −33.1528 | 47.1948 | 39.6159 | −307.406 | −219.668 | 323.919 | ||||||||||||||||||
1.19 | −9.71106 | −11.8693 | 62.3048 | 93.6186 | 115.264 | 163.882 | −294.291 | −102.119 | −909.136 | ||||||||||||||||||
1.20 | −9.64751 | −11.8379 | 61.0744 | −72.0672 | 114.206 | −61.6914 | −280.496 | −102.865 | 695.269 | ||||||||||||||||||
See next 80 embeddings (of 191 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(983\) | \(1\) |
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 | 983.6.a.a | ✓ | 191 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
983.6.a.a | ✓ | 191 | 1.a | even | 1 | 1 | trivial |