Properties

Label 1027.6.a.d
Level $1027$
Weight $6$
Character orbit 1027.a
Self dual yes
Analytic conductor $164.714$
Analytic rank $0$
Dimension $100$
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] = [1027,6,Mod(1,1027)] 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("1027.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1027, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")
 
Level: \( N \) \(=\) \( 1027 = 13 \cdot 79 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1027.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [100] 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: \(164.714182948\)
Analytic rank: \(0\)
Dimension: \(100\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 100 q + 32 q^{2} + 64 q^{3} + 1664 q^{4} + 193 q^{5} - 109 q^{6} + 304 q^{7} + 1176 q^{8} + 8698 q^{9} + 967 q^{10} + 558 q^{11} + 3056 q^{12} - 16900 q^{13} + 3555 q^{14} + 3652 q^{15} + 27080 q^{16} + 8143 q^{17}+ \cdots - 202346 q^{99}+O(q^{100}) \) 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 −11.1749 9.16423 92.8774 3.79191 −102.409 112.843 −680.296 −159.017 −42.3741
1.2 −10.8720 0.339250 86.2004 65.1415 −3.68833 −9.12082 −589.267 −242.885 −708.218
1.3 −10.3690 −24.1709 75.5172 −11.9463 250.629 160.196 −451.232 341.233 123.872
1.4 −10.3426 −11.2234 74.9703 −51.9604 116.080 −232.920 −444.427 −117.035 537.408
1.5 −10.2350 10.4814 72.7545 107.503 −107.277 −198.297 −417.121 −133.139 −1100.29
1.6 −10.2013 29.5745 72.0667 −34.5870 −301.698 −103.423 −408.732 631.649 352.833
1.7 −10.0579 −6.46262 69.1619 −93.3331 65.0006 −7.09321 −373.772 −201.234 938.737
1.8 −9.93742 24.7264 66.7524 −105.045 −245.717 −55.5573 −345.349 368.394 1043.88
1.9 −9.88261 19.6005 65.6659 87.7435 −193.704 121.764 −332.707 141.180 −867.134
1.10 −9.45055 −18.9808 57.3129 −43.8158 179.379 239.424 −239.221 117.272 414.084
1.11 −9.34346 10.8318 55.3002 −46.1094 −101.207 1.90904 −217.705 −125.671 430.821
1.12 −8.92494 −4.90887 47.6545 −7.04259 43.8113 −28.1252 −139.715 −218.903 62.8547
1.13 −8.84537 −18.8653 46.2406 54.8723 166.871 −196.721 −125.963 112.901 −485.366
1.14 −8.61605 10.4940 42.2363 43.0160 −90.4168 −77.5635 −88.1964 −132.876 −370.628
1.15 −8.57103 −30.6253 41.4625 −10.2210 262.491 33.2683 −81.1032 694.912 87.6045
1.16 −8.56226 30.4995 41.3122 60.6365 −261.144 −53.0750 −79.7336 687.219 −519.185
1.17 −8.11407 14.8043 33.8382 −47.6759 −120.124 172.062 −14.9153 −23.8315 386.846
1.18 −7.94152 −22.0554 31.0677 −70.9406 175.154 −18.0005 7.40355 243.442 563.376
1.19 −7.06720 22.3064 17.9453 −52.2982 −157.644 −247.619 99.3272 254.575 369.602
1.20 −7.04277 16.8613 17.6007 5.52044 −118.750 145.925 101.411 41.3020 −38.8792
See all 100 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1.100
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(13\) \( +1 \)
\(79\) \( -1 \)

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 1027.6.a.d ✓ 100
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1027.6.a.d ✓ 100 1.a even 1 1 trivial