Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [83,12,Mod(1,83)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(83, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("83.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 83 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 83.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: | \(63.7724839864\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
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 | −84.6320 | 725.642 | 5114.57 | −138.417 | −61412.5 | −14766.5 | −259530. | 349410. | 11714.5 | ||||||||||||||||||
1.2 | −80.2968 | 299.624 | 4399.57 | −9801.24 | −24058.9 | −79629.7 | −188824. | −87372.4 | 787008. | ||||||||||||||||||
1.3 | −76.8174 | −698.255 | 3852.92 | −1497.23 | 53638.2 | −37606.2 | −138649. | 310413. | 115013. | ||||||||||||||||||
1.4 | −75.1515 | 310.620 | 3599.76 | −3331.75 | −23343.6 | 22846.3 | −116617. | −80662.3 | 250387. | ||||||||||||||||||
1.5 | −74.8322 | −175.191 | 3551.87 | 481.582 | 13109.9 | 71848.6 | −112538. | −146455. | −36037.9 | ||||||||||||||||||
1.6 | −72.0004 | −662.974 | 3136.06 | 7943.35 | 47734.4 | 65761.4 | −78341.0 | 262387. | −571924. | ||||||||||||||||||
1.7 | −61.6711 | −219.979 | 1755.33 | −9872.64 | 13566.4 | −39761.8 | 18049.5 | −128756. | 608857. | ||||||||||||||||||
1.8 | −56.1374 | −353.575 | 1103.41 | 13945.8 | 19848.8 | −19965.2 | 53026.9 | −52131.4 | −782881. | ||||||||||||||||||
1.9 | −55.4460 | 550.444 | 1026.26 | 6117.02 | −30519.9 | −54173.9 | 56651.6 | 125842. | −339164. | ||||||||||||||||||
1.10 | −49.6278 | −218.214 | 414.923 | −1461.75 | 10829.5 | 41649.1 | 81046.1 | −129530. | 72543.5 | ||||||||||||||||||
1.11 | −38.6686 | 427.650 | −552.737 | 6694.69 | −16536.6 | 66374.6 | 100567. | 5737.36 | −258874. | ||||||||||||||||||
1.12 | −36.2955 | −411.095 | −730.638 | 9845.98 | 14920.9 | −576.671 | 100852. | −8148.14 | −357365. | ||||||||||||||||||
1.13 | −27.3201 | 389.394 | −1301.61 | −8154.66 | −10638.3 | −30368.3 | 91511.7 | −25519.7 | 222786. | ||||||||||||||||||
1.14 | −17.6153 | −304.962 | −1737.70 | −3502.17 | 5372.00 | −76614.1 | 66686.3 | −84145.3 | 61691.8 | ||||||||||||||||||
1.15 | −10.3628 | −25.0784 | −1940.61 | −11152.5 | 259.883 | 62955.9 | 41333.2 | −176518. | 115571. | ||||||||||||||||||
1.16 | −10.3472 | −687.970 | −1940.93 | −11758.9 | 7118.59 | −46300.0 | 41274.4 | 296156. | 121672. | ||||||||||||||||||
1.17 | −3.34813 | 588.225 | −2036.79 | −2172.37 | −1969.45 | 32142.0 | 13676.4 | 168862. | 7273.36 | ||||||||||||||||||
1.18 | 5.69141 | 560.569 | −2015.61 | −1354.87 | 3190.43 | 2723.03 | −23127.7 | 137091. | −7711.12 | ||||||||||||||||||
1.19 | 11.0295 | −323.150 | −1926.35 | 7514.61 | −3564.17 | 45.2205 | −43835.0 | −72721.2 | 82882.2 | ||||||||||||||||||
1.20 | 16.6341 | −475.219 | −1771.31 | −9331.09 | −7904.85 | 535.476 | −63530.9 | 48685.8 | −155215. | ||||||||||||||||||
See all 34 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(83\) | \(-1\) |
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 | 83.12.a.a | ✓ | 34 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
83.12.a.a | ✓ | 34 | 1.a | even | 1 | 1 | trivial |