Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,4,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(85.0217523183\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
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 | −5.64162 | −7.12045 | 23.8278 | 12.2922 | 40.1708 | 10.9151 | −89.2945 | 23.7008 | −69.3477 | ||||||||||||||||||
1.2 | −5.40673 | −0.868288 | 21.2327 | −21.2610 | 4.69460 | −2.80805 | −71.5459 | −26.2461 | 114.953 | ||||||||||||||||||
1.3 | −5.33631 | −6.68713 | 20.4762 | −7.16207 | 35.6846 | 10.7265 | −66.5769 | 17.7177 | 38.2190 | ||||||||||||||||||
1.4 | −5.29699 | 7.09451 | 20.0581 | −14.8169 | −37.5796 | −28.7336 | −63.8717 | 23.3321 | 78.4849 | ||||||||||||||||||
1.5 | −5.25982 | 7.15979 | 19.6657 | −3.23464 | −37.6592 | 13.6207 | −61.3597 | 24.2625 | 17.0137 | ||||||||||||||||||
1.6 | −5.03190 | −2.13656 | 17.3200 | 17.2575 | 10.7510 | 25.2731 | −46.8972 | −22.4351 | −86.8378 | ||||||||||||||||||
1.7 | −4.96967 | 4.89807 | 16.6976 | 5.95481 | −24.3418 | 15.7482 | −43.2240 | −3.00887 | −29.5934 | ||||||||||||||||||
1.8 | −4.71456 | −2.68555 | 14.2271 | −6.70082 | 12.6612 | −31.9614 | −29.3581 | −19.7878 | 31.5915 | ||||||||||||||||||
1.9 | −4.63574 | −1.60774 | 13.4901 | 19.3385 | 7.45306 | −5.00186 | −25.4508 | −24.4152 | −89.6483 | ||||||||||||||||||
1.10 | −4.59373 | 3.62650 | 13.1024 | −18.1051 | −16.6592 | 32.3039 | −23.4390 | −13.8485 | 83.1700 | ||||||||||||||||||
1.11 | −4.50745 | −6.76078 | 12.3171 | 12.7660 | 30.4739 | −21.9914 | −19.4592 | 18.7082 | −57.5420 | ||||||||||||||||||
1.12 | −4.48446 | −6.75386 | 12.1104 | −4.87147 | 30.2874 | −3.19104 | −18.4329 | 18.6146 | 21.8459 | ||||||||||||||||||
1.13 | −4.43460 | −0.0589157 | 11.6657 | 6.10695 | 0.261268 | −16.7287 | −16.2560 | −26.9965 | −27.0819 | ||||||||||||||||||
1.14 | −4.26168 | 7.45225 | 10.1619 | 9.79132 | −31.7591 | −16.2075 | −9.21354 | 28.5360 | −41.7275 | ||||||||||||||||||
1.15 | −4.17420 | 6.84332 | 9.42394 | 8.54373 | −28.5654 | 8.29120 | −5.94379 | 19.8310 | −35.6632 | ||||||||||||||||||
1.16 | −3.69212 | −0.963469 | 5.63174 | −13.7159 | 3.55724 | 27.6461 | 8.74389 | −26.0717 | 50.6405 | ||||||||||||||||||
1.17 | −3.64691 | 9.89090 | 5.29995 | −2.78497 | −36.0712 | −24.8287 | 9.84683 | 70.8299 | 10.1565 | ||||||||||||||||||
1.18 | −3.61438 | −9.63502 | 5.06371 | −13.1556 | 34.8246 | 22.8825 | 10.6128 | 65.8336 | 47.5492 | ||||||||||||||||||
1.19 | −3.45787 | 1.66598 | 3.95688 | −9.64680 | −5.76075 | −6.00852 | 13.9806 | −24.2245 | 33.3574 | ||||||||||||||||||
1.20 | −3.02808 | 7.31750 | 1.16924 | −4.74899 | −22.1579 | 3.39383 | 20.6841 | 26.5458 | 14.3803 | ||||||||||||||||||
See all 77 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(11\) | \(1\) |
\(131\) | \(-1\) |
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 | 1441.4.a.a | ✓ | 77 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1441.4.a.a | ✓ | 77 | 1.a | even | 1 | 1 | trivial |