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Properties

Label 795.2.w.a
Level $795$
Weight $2$
Character orbit 795.w
Analytic conductor $6.348$
Analytic rank $0$
Dimension $336$
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] = [795,2,Mod(4,795)] 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("795.4"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(795, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 13, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 795 = 3 \cdot 5 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 795.w (of order \(26\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [336,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.34810696069\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 336 q - 4 q^{2} + 28 q^{3} - 32 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} - 28 q^{9} + 4 q^{10} + 4 q^{11} + 32 q^{12} - 2 q^{15} - 40 q^{16} + 9 q^{18} - 38 q^{20} - 4 q^{22} + 100 q^{23} + 12 q^{24} - 10 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −0.324531 + 2.67275i −0.885456 − 0.464723i −5.09640 − 1.25615i 2.07297 + 0.838323i 1.52945 − 2.21579i −4.80285 − 0.583171i 3.10186 − 8.17892i 0.568065 + 0.822984i −2.91337 + 5.26848i
4.2 −0.319541 + 2.63166i −0.885456 − 0.464723i −4.88162 − 1.20321i −1.54332 − 1.61807i 1.50593 − 2.18172i −1.15049 − 0.139695i 2.84621 − 7.50485i 0.568065 + 0.822984i 4.75136 − 3.54446i
4.3 −0.285952 + 2.35503i −0.885456 − 0.464723i −3.52251 − 0.868220i 0.194188 + 2.22762i 1.34763 − 1.95239i 2.48447 + 0.301669i 1.36948 − 3.61101i 0.568065 + 0.822984i −5.30164 − 0.179675i
4.4 −0.247676 + 2.03980i −0.885456 − 0.464723i −2.15754 − 0.531786i −2.21856 − 0.279289i 1.16725 − 1.69105i 4.15778 + 0.504846i 0.161836 − 0.426727i 0.568065 + 0.822984i 1.11918 − 4.45623i
4.5 −0.244167 + 2.01090i −0.885456 − 0.464723i −2.04221 − 0.503361i −1.54868 + 1.61294i 1.15071 − 1.66709i −1.13103 − 0.137332i 0.0742253 − 0.195716i 0.568065 + 0.822984i −2.86533 − 3.50807i
4.6 −0.234541 + 1.93162i −0.885456 − 0.464723i −1.73425 − 0.427454i 1.12317 − 1.93352i 1.10534 − 1.60137i −1.31866 − 0.160114i −0.147553 + 0.389065i 0.568065 + 0.822984i 3.47138 + 2.62303i
4.7 −0.190836 + 1.57168i −0.885456 − 0.464723i −0.491874 − 0.121236i 2.21117 + 0.332744i 0.899373 − 1.30297i 1.45911 + 0.177168i −0.838426 + 2.21075i 0.568065 + 0.822984i −0.944939 + 3.41175i
4.8 −0.136939 + 1.12779i −0.885456 − 0.464723i 0.688720 + 0.169754i −1.21971 − 1.87412i 0.645365 − 0.934972i −1.47000 − 0.178490i −1.09148 + 2.87799i 0.568065 + 0.822984i 2.28064 − 1.11894i
4.9 −0.128659 + 1.05960i −0.885456 − 0.464723i 0.835679 + 0.205976i 0.918483 − 2.03872i 0.606344 − 0.878441i 4.16541 + 0.505772i −1.08277 + 2.85503i 0.568065 + 0.822984i 2.04206 + 1.23553i
4.10 −0.103095 + 0.849063i −0.885456 − 0.464723i 1.23160 + 0.303563i −2.20738 + 0.357032i 0.485865 − 0.703898i −4.20984 − 0.511167i −0.991303 + 2.61385i 0.568065 + 0.822984i −0.0755732 − 1.91101i
4.11 −0.0958750 + 0.789601i −0.885456 − 0.464723i 1.32761 + 0.327225i 1.60289 + 1.55908i 0.451839 − 0.654602i 3.89905 + 0.473430i −0.949768 + 2.50433i 0.568065 + 0.822984i −1.38473 + 1.11617i
4.12 −0.0535016 + 0.440625i −0.885456 − 0.464723i 1.75060 + 0.431483i −1.28289 + 1.83144i 0.252142 − 0.365291i 2.14246 + 0.260141i −0.598573 + 1.57831i 0.568065 + 0.822984i −0.738343 − 0.663261i
4.13 −0.0162625 + 0.133934i −0.885456 − 0.464723i 1.92421 + 0.474275i 1.87181 − 1.22324i 0.0766417 − 0.111035i −1.88634 − 0.229043i −0.190498 + 0.502303i 0.568065 + 0.822984i 0.133392 + 0.270592i
4.14 0.00499503 − 0.0411378i −0.885456 − 0.464723i 1.94022 + 0.478220i 0.323800 + 2.21250i −0.0235406 + 0.0341044i −3.80737 − 0.462299i 0.0587540 − 0.154921i 0.568065 + 0.822984i 0.0926347 − 0.00226892i
4.15 0.00731032 − 0.0602059i −0.885456 − 0.464723i 1.93831 + 0.477751i −0.938765 − 2.02946i −0.0344520 + 0.0499124i −0.0395401 − 0.00480103i 0.0859453 − 0.226619i 0.568065 + 0.822984i −0.129048 + 0.0416832i
4.16 0.0516160 − 0.425096i −0.885456 − 0.464723i 1.76384 + 0.434748i 2.17241 + 0.529770i −0.243256 + 0.352417i −1.35378 − 0.164378i 0.579549 − 1.52814i 0.568065 + 0.822984i 0.337334 − 0.896136i
4.17 0.0900676 − 0.741773i −0.885456 − 0.464723i 1.39977 + 0.345012i −1.05227 − 1.97300i −0.424470 + 0.614951i 2.94457 + 0.357535i 0.911931 − 2.40456i 0.568065 + 0.822984i −1.55829 + 0.602840i
4.18 0.161879 − 1.33319i −0.885456 − 0.464723i 0.190689 + 0.0470007i −1.15915 + 1.91217i −0.762901 + 1.10525i 1.54481 + 0.187573i 1.04599 − 2.75804i 0.568065 + 0.822984i 2.36164 + 1.85490i
4.19 0.162756 − 1.34041i −0.885456 − 0.464723i 0.171661 + 0.0423107i 1.92710 + 1.13414i −0.767035 + 1.11124i 1.00080 + 0.121519i 1.04227 − 2.74824i 0.568065 + 0.822984i 1.83387 − 2.39853i
4.20 0.171007 − 1.40837i −0.885456 − 0.464723i −0.0123849 − 0.00305260i −1.99301 + 1.01386i −0.805923 + 1.16758i 0.150842 + 0.0183155i 0.999750 − 2.63612i 0.568065 + 0.822984i 1.08707 + 2.98028i
See next 80 embeddings (of 336 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.28
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
265.l even 26 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 795.2.w.a ✓ 336
5.b even 2 1 795.2.w.b yes 336
53.e even 26 1 795.2.w.b yes 336
265.l even 26 1 inner 795.2.w.a ✓ 336
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
795.2.w.a ✓ 336 1.a even 1 1 trivial
795.2.w.a ✓ 336 265.l even 26 1 inner
795.2.w.b yes 336 5.b even 2 1
795.2.w.b yes 336 53.e even 26 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{336} + 4 T_{2}^{335} + 52 T_{2}^{334} + 196 T_{2}^{333} + 1482 T_{2}^{332} + \cdots + 90\!\cdots\!89 \) acting on \(S_{2}^{\mathrm{new}}(795, [\chi])\). Copy content Toggle raw display