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Properties

Label 841.2.d.o
Level $841$
Weight $2$
Character orbit 841.d
Analytic conductor $6.715$
Analytic rank $0$
Dimension $36$
Inner twists $6$

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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] = [841,2,Mod(190,841)] 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("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.d (of order \(7\), degree \(6\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [36,2,2,-8,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.71541880999\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
190.1 −1.97339 − 0.950335i 0.0691206 − 0.0866745i 1.74416 + 2.18710i 2.97424 + 1.43232i −0.218772 + 0.105355i −1.85283 + 2.32338i −0.388648 − 1.70278i 0.664828 + 2.91280i −4.50816 − 5.65305i
190.2 −1.62315 − 0.781668i −0.871284 + 1.09256i 0.776635 + 0.973869i 1.26508 + 0.609230i 2.26824 − 1.09233i 2.20280 − 2.76223i 0.302418 + 1.32498i 0.233021 + 1.02093i −1.57720 − 1.97774i
190.3 0.460625 + 0.221825i −1.67878 + 2.10513i −1.08401 − 1.35931i −1.98557 − 0.956199i −1.24026 + 0.597278i −0.811822 + 1.01799i −0.425324 − 1.86347i −0.945686 − 4.14332i −0.702494 − 0.880899i
190.4 0.771081 + 0.371333i 1.66407 − 2.08668i −0.790302 − 0.991007i 2.53454 + 1.22057i 2.05799 − 0.991075i −0.478052 + 0.599459i −0.622276 − 2.72637i −0.917539 − 4.02000i 1.50110 + 1.88232i
190.5 1.75304 + 0.844219i −1.41628 + 1.77596i 1.11346 + 1.39624i −2.89865 − 1.39592i −3.98209 + 1.91767i −1.57757 + 1.97820i −0.0927185 − 0.406226i −0.480617 − 2.10572i −3.90299 − 4.89420i
190.6 2.41373 + 1.16239i 0.986173 − 1.23662i 3.22798 + 4.04776i −0.0877054 − 0.0422367i 3.81780 − 1.83856i 0.0235094 − 0.0294798i 1.89411 + 8.29864i 0.110867 + 0.485740i −0.162602 − 0.203896i
571.1 −1.97339 + 0.950335i 0.0691206 + 0.0866745i 1.74416 − 2.18710i 2.97424 − 1.43232i −0.218772 − 0.105355i −1.85283 − 2.32338i −0.388648 + 1.70278i 0.664828 − 2.91280i −4.50816 + 5.65305i
571.2 −1.62315 + 0.781668i −0.871284 − 1.09256i 0.776635 − 0.973869i 1.26508 − 0.609230i 2.26824 + 1.09233i 2.20280 + 2.76223i 0.302418 − 1.32498i 0.233021 − 1.02093i −1.57720 + 1.97774i
571.3 0.460625 − 0.221825i −1.67878 − 2.10513i −1.08401 + 1.35931i −1.98557 + 0.956199i −1.24026 − 0.597278i −0.811822 − 1.01799i −0.425324 + 1.86347i −0.945686 + 4.14332i −0.702494 + 0.880899i
571.4 0.771081 − 0.371333i 1.66407 + 2.08668i −0.790302 + 0.991007i 2.53454 − 1.22057i 2.05799 + 0.991075i −0.478052 − 0.599459i −0.622276 + 2.72637i −0.917539 + 4.02000i 1.50110 − 1.88232i
571.5 1.75304 − 0.844219i −1.41628 − 1.77596i 1.11346 − 1.39624i −2.89865 + 1.39592i −3.98209 − 1.91767i −1.57757 − 1.97820i −0.0927185 + 0.406226i −0.480617 + 2.10572i −3.90299 + 4.89420i
571.6 2.41373 − 1.16239i 0.986173 + 1.23662i 3.22798 − 4.04776i −0.0877054 + 0.0422367i 3.81780 + 1.83856i 0.0235094 + 0.0294798i 1.89411 − 8.29864i 0.110867 − 0.485740i −0.162602 + 0.203896i
574.1 −1.67036 + 2.09456i −0.351961 + 1.54204i −1.15205 − 5.04747i 0.0606940 − 0.0761079i −2.64200 − 3.31296i −0.00839039 + 0.0367607i 7.66910 + 3.69324i 0.448891 + 0.216175i 0.0580320 + 0.254255i
574.2 −1.21314 + 1.52123i 0.505464 − 2.21458i −0.397390 − 1.74108i 2.00593 − 2.51536i 2.75569 + 3.45553i 0.563026 − 2.46678i −0.375409 − 0.180788i −1.94598 − 0.937134i 1.39296 + 6.10296i
574.3 −0.533605 + 0.669119i −0.593901 + 2.60205i 0.282055 + 1.23577i −1.75396 + 2.19939i −1.42417 − 1.78586i 0.170615 − 0.747513i −2.51954 − 1.21335i −3.71504 − 1.78907i −0.535736 − 2.34721i
574.4 −0.318763 + 0.399716i 0.599151 − 2.62505i 0.386879 + 1.69503i 1.37406 − 1.72301i 0.858287 + 1.07626i 0.289736 − 1.26942i −1.72210 − 0.829321i −3.82900 − 1.84395i 0.250717 + 1.09846i
574.5 1.12326 − 1.40852i 0.310958 − 1.36239i −0.277178 − 1.21440i −0.875462 + 1.09779i −1.56967 − 1.96831i −0.786171 + 3.44444i 1.22446 + 0.589671i 0.943483 + 0.454358i 0.562896 + 2.46621i
574.6 1.36563 − 1.71244i −0.0246689 + 0.108081i −0.622482 − 2.72727i −2.05824 + 2.58095i 0.151395 + 0.189843i 0.661268 − 2.89721i −1.57360 − 0.757807i 2.69183 + 1.29632i 1.60894 + 7.04924i
605.1 −0.487387 + 2.13538i −0.0998822 + 0.0481007i −2.52038 − 1.21375i 0.734577 − 3.21839i −0.0540322 − 0.236731i 2.67742 − 1.28938i 1.08897 − 1.36552i −1.86281 + 2.33589i 6.51448 + 3.13721i
605.2 −0.400885 + 1.75639i 1.25904 − 0.606322i −1.12227 − 0.540457i 0.312449 − 1.36893i 0.560209 + 2.45444i −3.18314 + 1.53292i −0.847355 + 1.06255i −0.652911 + 0.818724i 2.27912 + 1.09757i
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 190.6
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.d even 7 5 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 841.2.d.o 36
29.b even 2 1 841.2.d.n 36
29.c odd 4 2 841.2.e.l 72
29.d even 7 1 841.2.a.g ✓ 6
29.d even 7 5 inner 841.2.d.o 36
29.e even 14 1 841.2.a.h yes 6
29.e even 14 5 841.2.d.n 36
29.f odd 28 2 841.2.b.d 12
29.f odd 28 10 841.2.e.l 72
87.h odd 14 1 7569.2.a.y 6
87.j odd 14 1 7569.2.a.bc 6
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
841.2.a.g ✓ 6 29.d even 7 1
841.2.a.h yes 6 29.e even 14 1
841.2.b.d 12 29.f odd 28 2
841.2.d.n 36 29.b even 2 1
841.2.d.n 36 29.e even 14 5
841.2.d.o 36 1.a even 1 1 trivial
841.2.d.o 36 29.d even 7 5 inner
841.2.e.l 72 29.c odd 4 2
841.2.e.l 72 29.f odd 28 10
7569.2.a.y 6 87.h odd 14 1
7569.2.a.bc 6 87.j odd 14 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{36} - 2 T_{2}^{35} + 12 T_{2}^{34} - 25 T_{2}^{33} + 103 T_{2}^{32} - 227 T_{2}^{31} + \cdots + 531441 \) acting on \(S_{2}^{\mathrm{new}}(841, [\chi])\). Copy content Toggle raw display