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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [107,6,Mod(1,107)] 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("107.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(107, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")
 
Level: \( N \) \(=\) \( 107 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 107.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: \(17.1610687200\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 4 q^{2} + 55 q^{3} + 464 q^{4} + 149 q^{5} + 201 q^{6} + 380 q^{7} - 21 q^{8} + 2652 q^{9} + 1432 q^{10} + 346 q^{11} + 2412 q^{12} + 3556 q^{13} + 319 q^{14} + 59 q^{15} + 8196 q^{16} + 3453 q^{17}+ \cdots - 274849 q^{99}+O(q^{100}) \) 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 −11.1900 26.0154 93.2168 −89.4753 −291.113 160.320 −685.018 433.799 1001.23
1.2 −10.3220 −28.4284 74.5430 65.9456 293.437 211.138 −439.128 565.171 −680.688
1.3 −9.30206 −9.05270 54.5283 −36.9593 84.2087 112.137 −209.559 −161.049 343.798
1.4 −7.76424 10.2850 28.2834 −107.516 −79.8549 −207.411 28.8569 −137.220 834.783
1.5 −7.72249 25.3126 27.6369 10.8311 −195.477 −140.870 33.6941 397.730 −83.6427
1.6 −7.49483 −21.3854 24.1724 42.0965 160.280 −205.351 58.6664 214.337 −315.506
1.7 −7.23961 21.2091 20.4119 68.1917 −153.546 192.882 83.8934 206.828 −493.681
1.8 −7.11314 −10.4350 18.5967 100.634 74.2253 52.8757 95.3392 −134.112 −715.823
1.9 −3.83200 2.24994 −17.3158 −35.2421 −8.62177 −151.485 188.978 −237.938 135.048
1.10 −3.15185 0.101753 −22.0659 45.8164 −0.320711 144.073 170.407 −242.990 −144.406
1.11 −0.124224 −14.1608 −31.9846 −68.5876 1.75911 −57.3855 7.94843 −42.4722 8.52024
1.12 −0.0979745 25.4709 −31.9904 5.55747 −2.49550 −68.6212 6.26943 405.768 −0.544490
1.13 0.698567 7.49406 −31.5120 −90.9802 5.23510 126.459 −44.3674 −186.839 −63.5557
1.14 0.977179 −10.0509 −31.0451 −39.6764 −9.82149 −177.503 −61.6064 −141.980 −38.7709
1.15 1.84567 21.1854 −28.5935 74.7674 39.1011 147.892 −111.835 205.819 137.996
1.16 2.72152 −17.8922 −24.5933 87.3977 −48.6939 −115.669 −154.020 77.1293 237.855
1.17 5.07882 −27.3104 −6.20560 −67.7452 −138.705 −83.6489 −194.039 502.858 −344.065
1.18 5.33046 −16.4278 −3.58615 −37.8306 −87.5676 175.502 −189.691 26.8713 −201.655
1.19 7.16602 −0.109775 19.3519 78.4571 −0.786651 66.7505 −90.6368 −242.988 562.225
1.20 7.69693 29.6621 27.2427 94.3812 228.307 −200.413 −36.6168 636.840 726.445
See all 25 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1.25
Significant digits:
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Atkin-Lehner signs

\( p \) Sign
\(107\) \( -1 \)

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 107.6.a.b ✓ 25
3.b odd 2 1 963.6.a.e 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
107.6.a.b ✓ 25 1.a even 1 1 trivial
963.6.a.e 25 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} - 4 T_{2}^{24} - 624 T_{2}^{23} + 2439 T_{2}^{22} + 168995 T_{2}^{21} - 646338 T_{2}^{20} + \cdots - 14\!\cdots\!28 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(107))\). Copy content Toggle raw display