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Properties

Label 790.2.p.a
Level $790$
Weight $2$
Character orbit 790.p
Analytic conductor $6.308$
Analytic rank $0$
Dimension $480$
Inner twists $4$

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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(89,790)] 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("790.89"); 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([13, 22])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 790 = 2 \cdot 5 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 790.p (of order \(26\), degree \(12\), 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: \(6.30818175968\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(40\) over \(\Q(\zeta_{26})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{26}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 480 q + 40 q^{4} + 4 q^{6} + 48 q^{9} - 4 q^{10} - 8 q^{11} - 8 q^{14} - 8 q^{15} - 40 q^{16} + 16 q^{19} + 52 q^{21} + 48 q^{24} - 14 q^{25} - 20 q^{29} + 20 q^{30} - 68 q^{31} + 70 q^{35} - 48 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
89.1 −0.935016 + 0.354605i −1.54570 − 2.94509i 0.748511 − 0.663123i 0.655159 + 2.13794i 2.48960 + 2.20559i −0.0847863 − 0.161547i −0.464723 + 0.885456i −4.58016 + 6.63551i −1.37071 − 1.76668i
89.2 −0.935016 + 0.354605i −1.34511 − 2.56289i 0.748511 − 0.663123i −2.22997 − 0.165084i 2.16651 + 1.91936i −0.671711 − 1.27984i −0.464723 + 0.885456i −3.05489 + 4.42577i 2.14359 − 0.636401i
89.3 −0.935016 + 0.354605i −1.28703 − 2.45222i 0.748511 − 0.663123i 1.76570 − 1.37197i 2.07296 + 1.83648i −0.877281 − 1.67152i −0.464723 + 0.885456i −2.65277 + 3.84321i −1.16445 + 1.90894i
89.4 −0.935016 + 0.354605i −1.20939 − 2.30430i 0.748511 − 0.663123i −0.809956 − 2.08422i 1.94791 + 1.72570i 2.41032 + 4.59248i −0.464723 + 0.885456i −2.14296 + 3.10462i 1.49640 + 1.66156i
89.5 −0.935016 + 0.354605i −0.910349 − 1.73453i 0.748511 − 0.663123i −2.15193 − 0.607601i 1.46626 + 1.29900i 0.157037 + 0.299209i −0.464723 + 0.885456i −0.475649 + 0.689096i 2.22755 − 0.194970i
89.6 −0.935016 + 0.354605i −0.606894 − 1.15634i 0.748511 − 0.663123i −0.413079 + 2.19758i 0.977499 + 0.865988i −1.42538 − 2.71584i −0.464723 + 0.885456i 0.735394 − 1.06540i −0.393038 − 2.20125i
89.7 −0.935016 + 0.354605i −0.577452 − 1.10024i 0.748511 − 0.663123i −0.951806 − 2.02338i 0.930078 + 0.823977i −1.64166 − 3.12792i −0.464723 + 0.885456i 0.827112 − 1.19828i 1.60745 + 1.55438i
89.8 −0.935016 + 0.354605i −0.554697 − 1.05689i 0.748511 − 0.663123i 1.22445 − 1.87102i 0.893428 + 0.791508i 1.12968 + 2.15243i −0.464723 + 0.885456i 0.894874 − 1.29645i −0.481405 + 2.18363i
89.9 −0.935016 + 0.354605i −0.265462 − 0.505796i 0.748511 − 0.663123i 2.02932 + 0.939078i 0.427569 + 0.378793i 0.298074 + 0.567933i −0.464723 + 0.885456i 1.51884 − 2.20041i −2.23045 − 0.158447i
89.10 −0.935016 + 0.354605i −0.229775 − 0.437799i 0.748511 − 0.663123i −1.31779 + 1.80650i 0.370089 + 0.327870i 1.16377 + 2.21737i −0.464723 + 0.885456i 1.56532 − 2.26776i 0.591561 − 2.15640i
89.11 −0.935016 + 0.354605i 0.0188625 + 0.0359395i 0.748511 − 0.663123i 2.18821 + 0.460127i −0.0303811 − 0.0269153i −1.31726 − 2.50982i −0.464723 + 0.885456i 1.70326 − 2.46760i −2.20918 + 0.345725i
89.12 −0.935016 + 0.354605i 0.252699 + 0.481477i 0.748511 − 0.663123i −2.23525 + 0.0604503i −0.407012 − 0.360581i 0.930212 + 1.77237i −0.464723 + 0.885456i 1.53623 − 2.22561i 2.06856 − 0.849153i
89.13 −0.935016 + 0.354605i 0.430282 + 0.819835i 0.748511 − 0.663123i 1.43501 + 1.71486i −0.693038 − 0.613978i 1.96805 + 3.74980i −0.464723 + 0.885456i 1.21721 − 1.76343i −1.94986 − 1.09456i
89.14 −0.935016 + 0.354605i 0.505935 + 0.963979i 0.748511 − 0.663123i 1.34520 − 1.78618i −0.814889 − 0.721929i −0.409530 − 0.780295i −0.464723 + 0.885456i 1.03091 − 1.49353i −0.624394 + 2.14712i
89.15 −0.935016 + 0.354605i 0.702908 + 1.33928i 0.748511 − 0.663123i −1.65555 − 1.50305i −1.13215 − 1.00299i 1.42088 + 2.70726i −0.464723 + 0.885456i 0.404604 − 0.586170i 2.08096 + 0.818306i
89.16 −0.935016 + 0.354605i 0.897544 + 1.71013i 0.748511 − 0.663123i −2.03041 + 0.936705i −1.44564 − 1.28072i −1.56210 − 2.97633i −0.464723 + 0.885456i −0.414756 + 0.600878i 1.56631 − 1.59583i
89.17 −0.935016 + 0.354605i 1.02438 + 1.95179i 0.748511 − 0.663123i 1.49905 + 1.65917i −1.64992 − 1.46170i −1.08667 − 2.07048i −0.464723 + 0.885456i −1.05593 + 1.52978i −1.98999 − 1.01978i
89.18 −0.935016 + 0.354605i 1.05380 + 2.00785i 0.748511 − 0.663123i −1.04203 − 1.97842i −1.69731 − 1.50369i 0.156322 + 0.297847i −0.464723 + 0.885456i −1.21676 + 1.76279i 1.67588 + 1.48035i
89.19 −0.935016 + 0.354605i 1.21854 + 2.32174i 0.748511 − 0.663123i 0.333822 + 2.21101i −1.96265 − 1.73876i −0.731483 − 1.39372i −0.464723 + 0.885456i −2.20142 + 3.18931i −1.09616 − 1.94895i
89.20 −0.935016 + 0.354605i 1.49746 + 2.85317i 0.748511 − 0.663123i 2.12254 − 0.703426i −2.41189 − 2.13675i 2.03241 + 3.87243i −0.464723 + 0.885456i −4.19398 + 6.07603i −1.73517 + 1.41038i
See next 80 embeddings (of 480 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 89.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
79.e even 13 1 inner
395.p even 26 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 790.2.p.a ✓ 480
5.b even 2 1 inner 790.2.p.a ✓ 480
79.e even 13 1 inner 790.2.p.a ✓ 480
395.p even 26 1 inner 790.2.p.a ✓ 480
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
790.2.p.a ✓ 480 1.a even 1 1 trivial
790.2.p.a ✓ 480 5.b even 2 1 inner
790.2.p.a ✓ 480 79.e even 13 1 inner
790.2.p.a ✓ 480 395.p even 26 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(790, [\chi])\).