↑

Properties

Label 181.4.a.c
Level $181$
Weight $4$
Character orbit 181.a
Self dual yes
Analytic conductor $10.679$
Analytic rank $0$
Dimension $25$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [181,4,Mod(1,181)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("181.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(181, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 181 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 181.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [25] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(10.6793457110\)
Analytic rank: \(0\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 7 q^{2} + 19 q^{3} + 125 q^{4} + 26 q^{5} + 31 q^{6} + 31 q^{7} + 87 q^{8} + 284 q^{9} + 49 q^{10} + 339 q^{11} + 140 q^{12} + 28 q^{13} + 257 q^{14} + 170 q^{15} + 605 q^{16} + 242 q^{17} + 170 q^{18}+ \cdots + 6817 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.38021 −8.39274 20.9466 8.53698 45.1546 11.8955 −69.6554 43.4380 −45.9307
1.2 −4.58430 −0.530204 13.0158 −22.0528 2.43061 −30.2751 −22.9939 −26.7189 101.097
1.3 −4.55492 9.92373 12.7473 −7.20507 −45.2018 −30.4040 −21.6234 71.4805 32.8185
1.4 −4.54441 7.98998 12.6516 11.5947 −36.3097 19.1755 −21.1389 36.8398 −52.6908
1.5 −4.07986 2.75943 8.64526 −2.82753 −11.2581 10.6868 −2.63257 −19.3855 11.5359
1.6 −4.07076 −5.55637 8.57108 4.57188 22.6186 −10.8014 −2.32474 3.87320 −18.6110
1.7 −3.54983 −2.12873 4.60127 20.9148 7.55663 34.8436 12.0649 −22.4685 −74.2439
1.8 −1.49508 −2.28327 −5.76474 −13.0303 3.41367 2.13573 20.5794 −21.7867 19.4813
1.9 −1.45128 8.47156 −5.89377 13.7766 −12.2946 6.19849 20.1638 44.7673 −19.9937
1.10 −1.04213 3.92132 −6.91396 −14.2170 −4.08653 −12.1784 15.5423 −11.6232 14.8160
1.11 −0.839976 −3.95848 −7.29444 −8.74367 3.32503 −31.1625 12.8470 −11.3304 7.34448
1.12 −0.739807 −1.23966 −7.45269 20.2090 0.917111 −14.4643 11.4320 −25.4632 −14.9508
1.13 0.503023 5.96579 −7.74697 −3.03913 3.00093 35.4676 −7.92109 8.59067 −1.52875
1.14 0.863777 −8.52727 −7.25389 −9.78803 −7.36567 −22.5059 −13.1760 45.7144 −8.45468
1.15 1.62427 −5.63846 −5.36176 9.74180 −9.15835 6.98620 −21.7030 4.79218 15.8233
1.16 1.75078 −6.34322 −4.93476 −16.8452 −11.1056 16.5089 −22.6460 13.2364 −29.4923
1.17 2.21916 7.75938 −3.07535 10.6225 17.2193 −13.0028 −24.5779 33.2079 23.5729
1.18 3.31947 5.28268 3.01886 20.1700 17.5357 15.7597 −16.5347 0.906734 66.9537
1.19 3.59304 10.1516 4.90992 −5.97197 36.4750 11.1345 −11.1028 76.0544 −21.4575
1.20 4.13372 −0.465873 9.08768 7.01840 −1.92579 21.3765 4.49616 −26.7830 29.0121
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(181\) \( +1 \)

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 181.4.a.c ✓ 25
3.b odd 2 1 1629.4.a.f 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
181.4.a.c ✓ 25 1.a even 1 1 trivial
1629.4.a.f 25 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} - 7 T_{2}^{24} - 138 T_{2}^{23} + 1014 T_{2}^{22} + 8085 T_{2}^{21} - 63408 T_{2}^{20} + \cdots - 18978701312 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(181))\). Copy content Toggle raw display