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Properties

Label 787.4.a.b
Level $787$
Weight $4$
Character orbit 787.a
Self dual yes
Analytic conductor $46.435$
Analytic rank $0$
Dimension $103$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [787,4,Mod(1,787)] 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("787.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 787 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 787.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [103] 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: \(46.4345031745\)
Analytic rank: \(0\)
Dimension: \(103\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 103 q + 27 q^{2} + 25 q^{3} + 439 q^{4} + 169 q^{5} + 45 q^{6} + 80 q^{7} + 327 q^{8} + 1114 q^{9} + 61 q^{10} + 241 q^{11} + 264 q^{12} + 291 q^{13} + 341 q^{14} + 278 q^{15} + 2003 q^{16} + 504 q^{17}+ \cdots + 6933 q^{99}+O(q^{100}) \) 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 −5.48296 −5.58479 22.0629 13.1189 30.6212 28.6728 −77.1062 4.18987 −71.9303
1.2 −5.47387 9.49495 21.9633 7.39060 −51.9741 −4.75530 −76.4331 63.1540 −40.4552
1.3 −5.19699 −5.68578 19.0087 −5.26889 29.5489 10.4069 −57.2122 5.32806 27.3824
1.4 −5.11569 0.250896 18.1702 −15.9271 −1.28350 −5.30543 −52.0277 −26.9371 81.4780
1.5 −5.06870 5.10743 17.6917 −5.07363 −25.8880 −32.7384 −49.1242 −0.914152 25.7167
1.6 −4.95052 5.82419 16.5076 −7.62878 −28.8328 −17.1594 −42.1171 6.92120 37.7664
1.7 −4.93842 −9.56649 16.3880 19.7761 47.2434 −11.8006 −41.4234 64.5178 −97.6624
1.8 −4.87415 −5.16020 15.7573 8.00442 25.1516 −8.85635 −37.8104 −0.372310 −39.0147
1.9 −4.76060 5.10419 14.6634 4.27864 −24.2990 19.5515 −31.7216 −0.947230 −20.3689
1.10 −4.68995 −7.35902 13.9956 −6.30930 34.5134 −19.2375 −28.1191 27.1552 29.5903
1.11 −4.68502 3.75651 13.9494 22.0857 −17.5993 34.2107 −27.8730 −12.8886 −103.472
1.12 −4.63533 0.356003 13.4863 2.24804 −1.65019 15.4212 −25.4306 −26.8733 −10.4204
1.13 −4.49291 −0.641330 12.1863 12.9513 2.88144 −8.08445 −18.8086 −26.5887 −58.1891
1.14 −4.37274 6.07150 11.1208 −11.3448 −26.5491 7.75607 −13.6466 9.86307 49.6080
1.15 −4.26191 9.56249 10.1639 7.01573 −40.7545 26.4728 −9.22228 64.4412 −29.9004
1.16 −4.20535 −3.94586 9.68496 19.5461 16.5937 8.81107 −7.08586 −11.4302 −82.1982
1.17 −4.20325 −6.09175 9.66730 −9.51255 25.6051 0.938997 −7.00807 10.1094 39.9836
1.18 −3.89695 −8.63108 7.18622 −17.8453 33.6349 1.87975 3.17125 47.4955 69.5421
1.19 −3.77986 8.41249 6.28735 21.5021 −31.7980 −31.2345 6.47358 43.7699 −81.2748
1.20 −3.62911 1.51278 5.17042 −3.68800 −5.49005 −28.7927 10.2689 −24.7115 13.3841
See next 80 embeddings (of 103 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.103
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(787\) \( +1 \)

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 787.4.a.b ✓ 103
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
787.4.a.b ✓ 103 1.a even 1 1 trivial