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Properties

Label 11.8.c.a
Level $11$
Weight $8$
Character orbit 11.c
Analytic conductor $3.436$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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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] = [11,8,Mod(3,11)] 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("11.3"); S:= CuspForms(chi, 8); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 11.c (of order \(5\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.43623528033\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 3 q^{2} + 36 q^{3} - 505 q^{4} - 72 q^{5} + 853 q^{6} + 68 q^{7} - 4545 q^{8} + 1078 q^{9} + 4240 q^{10} + 5952 q^{11} + 11638 q^{12} - 16564 q^{13} - 29544 q^{14} + 68084 q^{15} + 13279 q^{16} - 65592 q^{17}+ \cdots - 20032696 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 −13.5536 + 9.84730i −14.4249 − 44.3951i 47.1778 − 145.198i 315.392 + 229.146i 632.682 + 459.670i 356.708 − 1097.83i 127.721 + 393.085i 6.46918 − 4.70013i −6531.19
3.2 −12.7113 + 9.23528i 16.6337 + 51.1934i 36.7318 − 113.049i −268.339 − 194.959i −684.221 − 497.116i −72.0370 + 221.707i −44.3449 − 136.480i −574.763 + 417.590i 5211.43
3.3 −1.19911 + 0.871205i 2.15176 + 6.62243i −38.8753 + 119.646i 171.086 + 124.301i −8.34968 − 6.06640i −463.381 + 1426.14i −116.247 − 357.771i 1730.09 − 1256.99i −313.442
3.4 0.987911 − 0.717759i −18.8902 − 58.1380i −39.0934 + 120.317i −339.439 − 246.617i −60.3909 − 43.8766i 312.595 − 962.069i 96.0385 + 295.576i −1253.87 + 910.990i −512.347
3.5 7.83171 − 5.69007i 23.5652 + 72.5261i −10.5954 + 32.6093i 9.68480 + 7.03642i 597.234 + 433.916i 520.681 − 1602.49i 485.474 + 1494.14i −2935.40 + 2132.69i 115.886
3.6 14.3633 − 10.4355i −6.74383 − 20.7554i 57.8489 − 178.041i 53.3657 + 38.7724i −313.456 − 227.739i −143.396 + 441.326i −324.804 − 999.643i 1384.01 − 1005.54i 1171.11
4.1 −13.5536 − 9.84730i −14.4249 + 44.3951i 47.1778 + 145.198i 315.392 − 229.146i 632.682 − 459.670i 356.708 + 1097.83i 127.721 − 393.085i 6.46918 + 4.70013i −6531.19
4.2 −12.7113 − 9.23528i 16.6337 − 51.1934i 36.7318 + 113.049i −268.339 + 194.959i −684.221 + 497.116i −72.0370 − 221.707i −44.3449 + 136.480i −574.763 − 417.590i 5211.43
4.3 −1.19911 − 0.871205i 2.15176 − 6.62243i −38.8753 − 119.646i 171.086 − 124.301i −8.34968 + 6.06640i −463.381 − 1426.14i −116.247 + 357.771i 1730.09 + 1256.99i −313.442
4.4 0.987911 + 0.717759i −18.8902 + 58.1380i −39.0934 − 120.317i −339.439 + 246.617i −60.3909 + 43.8766i 312.595 + 962.069i 96.0385 − 295.576i −1253.87 − 910.990i −512.347
4.5 7.83171 + 5.69007i 23.5652 − 72.5261i −10.5954 − 32.6093i 9.68480 − 7.03642i 597.234 − 433.916i 520.681 + 1602.49i 485.474 − 1494.14i −2935.40 − 2132.69i 115.886
4.6 14.3633 + 10.4355i −6.74383 + 20.7554i 57.8489 + 178.041i 53.3657 − 38.7724i −313.456 + 227.739i −143.396 − 441.326i −324.804 + 999.643i 1384.01 + 1005.54i 1171.11
5.1 −4.77944 − 14.7096i −26.0461 − 18.9236i −89.9749 + 65.3706i −44.2018 + 136.039i −153.873 + 473.572i −451.793 + 328.247i −210.025 − 152.592i −355.523 − 1094.19i 2212.34
5.2 −3.78266 − 11.6418i 65.2919 + 47.4374i −17.6695 + 12.8376i 31.6803 − 97.5020i 305.280 − 939.557i 601.350 − 436.906i −1051.31 − 763.821i 1336.91 + 4114.59i −1254.94
5.3 0.419581 + 1.29134i −22.7291 − 16.5137i 102.063 − 74.1529i 90.0532 − 277.155i 11.7880 − 36.2797i 205.463 − 149.277i 279.185 + 202.840i −431.909 − 1329.28i 395.685
5.4 2.40997 + 7.41712i 23.7466 + 17.2529i 54.3484 − 39.4864i −139.587 + 429.605i −70.7385 + 217.711i 40.1674 − 29.1833i 1231.45 + 894.704i −409.581 − 1260.56i −3522.83
5.5 5.72800 + 17.6290i −70.9612 − 51.5564i −174.417 + 126.721i −66.8497 + 205.742i 502.420 − 1546.29i −327.935 + 238.259i −1313.52 − 954.328i 1701.62 + 5237.04i −4009.94
5.6 5.78570 + 17.8065i 46.4061 + 33.7160i −180.045 + 130.810i 151.154 − 465.205i −331.874 + 1021.40i −544.422 + 395.546i −1432.12 − 1040.50i 340.938 + 1049.30i 9158.23
9.1 −4.77944 + 14.7096i −26.0461 + 18.9236i −89.9749 − 65.3706i −44.2018 − 136.039i −153.873 − 473.572i −451.793 − 328.247i −210.025 + 152.592i −355.523 + 1094.19i 2212.34
9.2 −3.78266 + 11.6418i 65.2919 − 47.4374i −17.6695 − 12.8376i 31.6803 + 97.5020i 305.280 + 939.557i 601.350 + 436.906i −1051.31 + 763.821i 1336.91 − 4114.59i −1254.94
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.6
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 11.8.c.a ✓ 24
3.b odd 2 1 99.8.f.a 24
11.c even 5 1 inner 11.8.c.a ✓ 24
11.c even 5 1 121.8.a.i 12
11.d odd 10 1 121.8.a.g 12
33.h odd 10 1 99.8.f.a 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
11.8.c.a ✓ 24 1.a even 1 1 trivial
11.8.c.a ✓ 24 11.c even 5 1 inner
99.8.f.a 24 3.b odd 2 1
99.8.f.a 24 33.h odd 10 1
121.8.a.g 12 11.d odd 10 1
121.8.a.i 12 11.c even 5 1

Hecke kernels

This newform subspace is the entire newspace \(S_{8}^{\mathrm{new}}(11, [\chi])\).