Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
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 | −2.46822 | −1.00000 | 4.09210 | 0.833166 | 2.46822 | −0.715489 | −5.16375 | 1.00000 | −2.05644 | ||||||||||||||||||
1.2 | −2.41406 | −1.00000 | 3.82770 | 1.38907 | 2.41406 | −5.15713 | −4.41218 | 1.00000 | −3.35331 | ||||||||||||||||||
1.3 | −2.30059 | −1.00000 | 3.29272 | −0.193972 | 2.30059 | 1.10356 | −2.97403 | 1.00000 | 0.446250 | ||||||||||||||||||
1.4 | −1.97908 | −1.00000 | 1.91674 | 3.55725 | 1.97908 | 2.67617 | 0.164776 | 1.00000 | −7.04007 | ||||||||||||||||||
1.5 | −1.55293 | −1.00000 | 0.411606 | −3.25042 | 1.55293 | 1.50369 | 2.46667 | 1.00000 | 5.04769 | ||||||||||||||||||
1.6 | −1.21952 | −1.00000 | −0.512778 | −1.58706 | 1.21952 | −3.41478 | 3.06438 | 1.00000 | 1.93545 | ||||||||||||||||||
1.7 | −1.18480 | −1.00000 | −0.596253 | −2.40127 | 1.18480 | −0.655760 | 3.07604 | 1.00000 | 2.84502 | ||||||||||||||||||
1.8 | −0.922410 | −1.00000 | −1.14916 | −0.0437394 | 0.922410 | 4.58186 | 2.90482 | 1.00000 | 0.0403457 | ||||||||||||||||||
1.9 | −0.891747 | −1.00000 | −1.20479 | 2.60961 | 0.891747 | −3.10366 | 2.85786 | 1.00000 | −2.32711 | ||||||||||||||||||
1.10 | −0.821645 | −1.00000 | −1.32490 | 1.58661 | 0.821645 | 1.25319 | 2.73189 | 1.00000 | −1.30363 | ||||||||||||||||||
1.11 | −0.236594 | −1.00000 | −1.94402 | 3.94072 | 0.236594 | −1.91925 | 0.933134 | 1.00000 | −0.932353 | ||||||||||||||||||
1.12 | 0.220817 | −1.00000 | −1.95124 | −3.79014 | −0.220817 | −3.98824 | −0.872503 | 1.00000 | −0.836928 | ||||||||||||||||||
1.13 | 0.736590 | −1.00000 | −1.45743 | −2.90793 | −0.736590 | −3.09183 | −2.54671 | 1.00000 | −2.14196 | ||||||||||||||||||
1.14 | 0.795328 | −1.00000 | −1.36745 | 2.82245 | −0.795328 | −3.74228 | −2.67823 | 1.00000 | 2.24477 | ||||||||||||||||||
1.15 | 0.799151 | −1.00000 | −1.36136 | 0.403932 | −0.799151 | 1.36573 | −2.68623 | 1.00000 | 0.322802 | ||||||||||||||||||
1.16 | 0.843162 | −1.00000 | −1.28908 | −2.14706 | −0.843162 | 4.16350 | −2.77323 | 1.00000 | −1.81032 | ||||||||||||||||||
1.17 | 1.73045 | −1.00000 | 0.994457 | 2.73352 | −1.73045 | −2.97598 | −1.74004 | 1.00000 | 4.73022 | ||||||||||||||||||
1.18 | 1.95682 | −1.00000 | 1.82914 | 0.334746 | −1.95682 | 4.67011 | −0.334351 | 1.00000 | 0.655037 | ||||||||||||||||||
1.19 | 2.12169 | −1.00000 | 2.50157 | 3.09428 | −2.12169 | −1.64576 | 1.06418 | 1.00000 | 6.56509 | ||||||||||||||||||
1.20 | 2.37194 | −1.00000 | 3.62611 | −0.369639 | −2.37194 | −3.46859 | 3.85703 | 1.00000 | −0.876762 | ||||||||||||||||||
See all 22 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(17\) | \(-1\) |
\(79\) | \(-1\) |
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 | 4029.2.a.f | ✓ | 22 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4029.2.a.f | ✓ | 22 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):
\( T_{2}^{22} - T_{2}^{21} - 31 T_{2}^{20} + 25 T_{2}^{19} + 409 T_{2}^{18} - 251 T_{2}^{17} - 2996 T_{2}^{16} + \cdots - 106 \) |
\( T_{5}^{22} - T_{5}^{21} - 64 T_{5}^{20} + 62 T_{5}^{19} + 1723 T_{5}^{18} - 1617 T_{5}^{17} + \cdots - 1435 \) |