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Properties

Label 19.10.c.a
Level $19$
Weight $10$
Character orbit 19.c
Analytic conductor $9.786$
Analytic rank $0$
Dimension $28$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [19,10,Mod(7,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.7"); S:= CuspForms(chi, 10); N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 19.c (of order \(3\), degree \(2\), 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: \(9.78568088711\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −19.9646 − 34.5797i 53.5081 + 92.6787i −541.171 + 937.336i −90.9465 − 157.524i 2136.54 − 3700.59i 6421.38 22773.3 4115.27 − 7127.85i −3631.42 + 6289.81i
7.2 −17.0666 − 29.5602i −104.220 − 180.515i −326.535 + 565.575i 1253.36 + 2170.89i −3557.37 + 6161.54i 4067.64 4815.16 −11882.3 + 20580.7i 42781.2 − 74099.2i
7.3 −16.3218 − 28.2702i −65.4143 − 113.301i −276.801 + 479.434i −805.880 − 1395.83i −2135.35 + 3698.54i −7030.62 1358.05 1283.45 − 2223.00i −26306.8 + 45564.7i
7.4 −12.6406 − 21.8941i 88.4986 + 153.284i −63.5673 + 110.102i 498.878 + 864.082i 2237.34 − 3875.19i −9657.65 −9729.83 −5822.52 + 10084.9i 12612.2 − 21845.0i
7.5 −6.82378 − 11.8191i −35.4198 − 61.3488i 162.872 − 282.103i −572.036 − 990.795i −483.393 + 837.262i 5106.36 −11433.2 7332.38 − 12700.1i −7806.89 + 13521.9i
7.6 −3.83779 − 6.64725i 111.749 + 193.554i 226.543 − 392.383i −746.119 − 1292.32i 857.737 − 1485.64i 8355.84 −7407.60 −15134.0 + 26212.9i −5726.90 + 9919.28i
7.7 −3.46328 − 5.99858i −8.56249 − 14.8307i 232.011 − 401.855i 781.382 + 1353.39i −59.3086 + 102.726i −83.0972 −6760.48 9694.87 − 16792.0i 5412.29 − 9374.37i
7.8 3.32582 + 5.76048i −131.258 − 227.345i 233.878 − 405.088i −77.5423 − 134.307i 873.077 − 1512.21i −3034.24 6516.98 −24615.6 + 42635.4i 515.783 − 893.362i
7.9 7.35932 + 12.7467i 42.7370 + 74.0227i 147.681 − 255.791i −1107.26 − 1917.83i −629.031 + 1089.51i −12185.9 11883.3 6188.59 − 10719.0i 16297.3 − 28227.8i
7.10 9.20750 + 15.9479i 85.3852 + 147.891i 86.4437 − 149.725i 795.817 + 1378.40i −1572.37 + 2723.42i 2900.36 12612.2 −4739.75 + 8209.49i −14655.0 + 25383.2i
7.11 10.9691 + 18.9991i −35.9517 − 62.2702i 15.3560 − 26.5973i 242.418 + 419.881i 788.718 − 1366.10i 1688.25 11906.2 7256.45 − 12568.5i −5318.24 + 9211.46i
7.12 17.0782 + 29.5803i −62.2446 − 107.811i −327.330 + 566.952i −952.067 − 1649.03i 2126.05 − 3682.43i 11028.1 −4872.73 2092.73 − 3624.71i 32519.2 − 56324.9i
7.13 19.4836 + 33.7465i 89.2835 + 154.644i −503.218 + 871.599i −249.322 − 431.838i −3479.12 + 6026.01i 698.529 −19266.8 −6101.58 + 10568.2i 9715.34 − 16827.5i
7.14 20.1948 + 34.9785i −65.0904 − 112.740i −559.662 + 969.363i 886.813 + 1536.00i 2628.98 − 4553.53i −9612.95 −24529.6 1367.97 − 2369.40i −35818.1 + 62038.7i
11.1 −19.9646 + 34.5797i 53.5081 − 92.6787i −541.171 − 937.336i −90.9465 + 157.524i 2136.54 + 3700.59i 6421.38 22773.3 4115.27 + 7127.85i −3631.42 − 6289.81i
11.2 −17.0666 + 29.5602i −104.220 + 180.515i −326.535 − 565.575i 1253.36 − 2170.89i −3557.37 − 6161.54i 4067.64 4815.16 −11882.3 − 20580.7i 42781.2 + 74099.2i
11.3 −16.3218 + 28.2702i −65.4143 + 113.301i −276.801 − 479.434i −805.880 + 1395.83i −2135.35 − 3698.54i −7030.62 1358.05 1283.45 + 2223.00i −26306.8 − 45564.7i
11.4 −12.6406 + 21.8941i 88.4986 − 153.284i −63.5673 − 110.102i 498.878 − 864.082i 2237.34 + 3875.19i −9657.65 −9729.83 −5822.52 − 10084.9i 12612.2 + 21845.0i
11.5 −6.82378 + 11.8191i −35.4198 + 61.3488i 162.872 + 282.103i −572.036 + 990.795i −483.393 − 837.262i 5106.36 −11433.2 7332.38 + 12700.1i −7806.89 − 13521.9i
11.6 −3.83779 + 6.64725i 111.749 − 193.554i 226.543 + 392.383i −746.119 + 1292.32i 857.737 + 1485.64i 8355.84 −7407.60 −15134.0 − 26212.9i −5726.90 − 9919.28i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.14
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 19.10.c.a ✓ 28
19.c even 3 1 inner 19.10.c.a ✓ 28
19.c even 3 1 361.10.a.e 14
19.d odd 6 1 361.10.a.f 14
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
19.10.c.a ✓ 28 1.a even 1 1 trivial
19.10.c.a ✓ 28 19.c even 3 1 inner
361.10.a.e 14 19.c even 3 1
361.10.a.f 14 19.d odd 6 1

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(19, [\chi])\).