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Properties

Label 790.2.m.f
Level $790$
Weight $2$
Character orbit 790.m
Analytic conductor $6.308$
Analytic rank $0$
Dimension $72$
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] = [790,2,Mod(21,790)] 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("790.21"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(790, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 18])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 790 = 2 \cdot 5 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 790.m (of order \(13\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [72,6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.30818175968\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{13})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{13}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 4 q^{7} + 6 q^{8} - 6 q^{9} - 6 q^{10} + 26 q^{13} - 4 q^{14} - 13 q^{15} - 6 q^{16} + 13 q^{17} + 6 q^{18} + 26 q^{19} + 6 q^{20} - 65 q^{21} + 26 q^{24} - 6 q^{25}+ \cdots + 67 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 0.748511 − 0.663123i −1.81000 + 2.62224i 0.120537 − 0.992709i 0.970942 − 0.239316i 0.384062 + 3.16303i −0.950357 + 1.37683i −0.568065 − 0.822984i −2.53623 − 6.68750i 0.568065 − 0.822984i
21.2 0.748511 − 0.663123i −1.11173 + 1.61062i 0.120537 − 0.992709i 0.970942 − 0.239316i 0.235896 + 1.94278i 2.20250 − 3.19087i −0.568065 − 0.822984i −0.294333 − 0.776092i 0.568065 − 0.822984i
21.3 0.748511 − 0.663123i −0.693940 + 1.00535i 0.120537 − 0.992709i 0.970942 − 0.239316i 0.147246 + 1.21268i −0.487496 + 0.706260i −0.568065 − 0.822984i 0.534648 + 1.40975i 0.568065 − 0.822984i
21.4 0.748511 − 0.663123i −0.165612 + 0.239930i 0.120537 − 0.992709i 0.970942 − 0.239316i 0.0351409 + 0.289411i −0.841216 + 1.21871i −0.568065 − 0.822984i 1.03368 + 2.72558i 0.568065 − 0.822984i
21.5 0.748511 − 0.663123i 0.802491 − 1.16261i 0.120537 − 0.992709i 0.970942 − 0.239316i −0.170279 − 1.40237i 0.324996 − 0.470838i −0.568065 − 0.822984i 0.356148 + 0.939084i 0.568065 − 0.822984i
21.6 0.748511 − 0.663123i 1.43979 − 2.08589i 0.120537 − 0.992709i 0.970942 − 0.239316i −0.305506 − 2.51607i 1.95781 − 2.83638i −0.568065 − 0.822984i −1.21415 − 3.20144i 0.568065 − 0.822984i
101.1 −0.568065 + 0.822984i −2.72313 + 0.671190i −0.354605 − 0.935016i 0.748511 + 0.663123i 0.994533 − 2.62237i −1.21235 + 0.298817i 0.970942 + 0.239316i 4.30855 − 2.26130i −0.970942 + 0.239316i
101.2 −0.568065 + 0.822984i −1.53247 + 0.377719i −0.354605 − 0.935016i 0.748511 + 0.663123i 0.559683 − 1.47576i 2.78542 − 0.686544i 0.970942 + 0.239316i −0.450588 + 0.236487i −0.970942 + 0.239316i
101.3 −0.568065 + 0.822984i −0.379984 + 0.0936575i −0.354605 − 0.935016i 0.748511 + 0.663123i 0.138777 − 0.365924i −1.49518 + 0.368530i 0.970942 + 0.239316i −2.52075 + 1.32299i −0.970942 + 0.239316i
101.4 −0.568065 + 0.822984i 1.01386 − 0.249895i −0.354605 − 0.935016i 0.748511 + 0.663123i −0.370281 + 0.976350i −1.10618 + 0.272649i 0.970942 + 0.239316i −1.69090 + 0.887451i −0.970942 + 0.239316i
101.5 −0.568065 + 0.822984i 1.86343 − 0.459293i −0.354605 − 0.935016i 0.748511 + 0.663123i −0.680555 + 1.79448i −4.75195 + 1.17125i 0.970942 + 0.239316i 0.605035 − 0.317547i −0.970942 + 0.239316i
101.6 −0.568065 + 0.822984i 1.98072 − 0.488203i −0.354605 − 0.935016i 0.748511 + 0.663123i −0.723393 + 1.90743i 2.87320 − 0.708179i 0.970942 + 0.239316i 1.02853 − 0.539816i −0.970942 + 0.239316i
131.1 −0.885456 − 0.464723i −0.319642 + 2.63249i 0.568065 + 0.822984i 0.354605 + 0.935016i 1.50641 − 2.18241i 0.239204 − 1.97002i −0.120537 − 0.992709i −3.91499 − 0.964959i 0.120537 − 0.992709i
131.2 −0.885456 − 0.464723i −0.293798 + 2.41964i 0.568065 + 0.822984i 0.354605 + 0.935016i 1.38461 − 2.00595i −0.266326 + 2.19340i −0.120537 − 0.992709i −2.85552 − 0.703822i 0.120537 − 0.992709i
131.3 −0.885456 − 0.464723i −0.203968 + 1.67983i 0.568065 + 0.822984i 0.354605 + 0.935016i 0.961262 − 1.39263i −0.494168 + 4.06984i −0.120537 − 0.992709i 0.132596 + 0.0326820i 0.120537 − 0.992709i
131.4 −0.885456 − 0.464723i −0.000468374 0.00385741i 0.568065 + 0.822984i 0.354605 + 0.935016i 0.00220735 − 0.00319790i −0.00785738 + 0.0647114i −0.120537 − 0.992709i 2.91281 + 0.717943i 0.120537 − 0.992709i
131.5 −0.885456 − 0.464723i 0.0333467 − 0.274635i 0.568065 + 0.822984i 0.354605 + 0.935016i −0.157156 + 0.227680i 0.185623 − 1.52874i −0.120537 − 0.992709i 2.83851 + 0.699631i 0.120537 − 0.992709i
131.6 −0.885456 − 0.464723i 0.309388 − 2.54804i 0.568065 + 0.822984i 0.354605 + 0.935016i −1.45808 + 2.11240i 0.514498 − 4.23727i −0.120537 − 0.992709i −3.48396 − 0.858718i 0.120537 − 0.992709i
141.1 0.970942 + 0.239316i −2.15960 + 1.91324i 0.885456 + 0.464723i −0.568065 + 0.822984i −2.55472 + 1.34082i 3.64329 − 3.22767i 0.748511 + 0.663123i 0.641784 − 5.28556i −0.748511 + 0.663123i
141.2 0.970942 + 0.239316i −1.23319 + 1.09251i 0.885456 + 0.464723i −0.568065 + 0.822984i −1.45881 + 0.765645i −2.02761 + 1.79631i 0.748511 + 0.663123i −0.0344313 + 0.283567i −0.748511 + 0.663123i
See all 72 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 21.6
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
79.e even 13 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 790.2.m.f ✓ 72
79.e even 13 1 inner 790.2.m.f ✓ 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
790.2.m.f ✓ 72 1.a even 1 1 trivial
790.2.m.f ✓ 72 79.e even 13 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{72} + 12 T_{3}^{70} + 13 T_{3}^{69} + 164 T_{3}^{68} + 187 T_{3}^{67} + 1527 T_{3}^{66} + \cdots + 2809 \) acting on \(S_{2}^{\mathrm{new}}(790, [\chi])\). Copy content Toggle raw display