Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
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 | −2.77862 | 1.96044 | 5.72072 | −1.21161 | −5.44733 | 1.22758 | −10.3385 | 0.843341 | 3.36659 | ||||||||||||||||||
1.2 | −2.75811 | −1.16707 | 5.60719 | −1.99614 | 3.21892 | −2.42048 | −9.94903 | −1.63794 | 5.50558 | ||||||||||||||||||
1.3 | −2.74408 | 1.08258 | 5.52999 | 4.29779 | −2.97068 | 1.02479 | −9.68658 | −1.82803 | −11.7935 | ||||||||||||||||||
1.4 | −2.74361 | −3.40606 | 5.52740 | −0.590422 | 9.34489 | −1.99716 | −9.67782 | 8.60122 | 1.61989 | ||||||||||||||||||
1.5 | −2.63043 | 0.0298964 | 4.91916 | −2.77768 | −0.0786403 | −4.82248 | −7.67864 | −2.99911 | 7.30650 | ||||||||||||||||||
1.6 | −2.60291 | 2.78039 | 4.77512 | −1.36371 | −7.23709 | −4.03414 | −7.22339 | 4.73056 | 3.54962 | ||||||||||||||||||
1.7 | −2.59099 | −0.493919 | 4.71322 | 1.04082 | 1.27974 | −3.08433 | −7.02991 | −2.75604 | −2.69675 | ||||||||||||||||||
1.8 | −2.57108 | 2.45924 | 4.61046 | 0.658521 | −6.32291 | 1.43884 | −6.71170 | 3.04787 | −1.69311 | ||||||||||||||||||
1.9 | −2.55845 | −2.16736 | 4.54566 | 2.09071 | 5.54507 | −1.08828 | −6.51294 | 1.69743 | −5.34897 | ||||||||||||||||||
1.10 | −2.55473 | −3.25140 | 4.52663 | 2.74770 | 8.30644 | 1.12543 | −6.45485 | 7.57160 | −7.01962 | ||||||||||||||||||
1.11 | −2.54629 | −1.60651 | 4.48361 | −2.62778 | 4.09064 | 1.52719 | −6.32399 | −0.419134 | 6.69110 | ||||||||||||||||||
1.12 | −2.37150 | 0.0708005 | 3.62401 | 3.28290 | −0.167903 | −0.427363 | −3.85135 | −2.99499 | −7.78539 | ||||||||||||||||||
1.13 | −2.34386 | 0.672591 | 3.49366 | 0.169027 | −1.57646 | 4.26981 | −3.50093 | −2.54762 | −0.396175 | ||||||||||||||||||
1.14 | −2.34025 | −2.24282 | 3.47677 | 1.33607 | 5.24876 | 2.78387 | −3.45602 | 2.03023 | −3.12673 | ||||||||||||||||||
1.15 | −2.33451 | 2.56074 | 3.44993 | 1.12501 | −5.97807 | −4.54116 | −3.38489 | 3.55739 | −2.62635 | ||||||||||||||||||
1.16 | −2.31791 | −1.39322 | 3.37270 | −1.41282 | 3.22936 | 3.95674 | −3.18178 | −1.05893 | 3.27480 | ||||||||||||||||||
1.17 | −2.27388 | 0.787573 | 3.17053 | −4.28008 | −1.79085 | 1.25028 | −2.66164 | −2.37973 | 9.73239 | ||||||||||||||||||
1.18 | −2.26494 | 1.60784 | 3.12995 | −1.10184 | −3.64166 | 0.234772 | −2.55928 | −0.414855 | 2.49560 | ||||||||||||||||||
1.19 | −2.21508 | 0.0631249 | 2.90657 | −0.959004 | −0.139827 | −0.280080 | −2.00812 | −2.99602 | 2.12427 | ||||||||||||||||||
1.20 | −2.20146 | −2.87956 | 2.84641 | 0.0712627 | 6.33923 | 3.68192 | −1.86333 | 5.29189 | −0.156882 | ||||||||||||||||||
See next 80 embeddings (of 149 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(23\) | \(1\) |
\(349\) | \(1\) |
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 | 8027.2.a.d | ✓ | 149 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8027.2.a.d | ✓ | 149 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{149} + 5 T_{2}^{148} - 204 T_{2}^{147} - 1050 T_{2}^{146} + 20289 T_{2}^{145} + 107741 T_{2}^{144} + \cdots - 164876704 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).