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Properties

Label 841.2.d.p
Level $841$
Weight $2$
Character orbit 841.d
Analytic conductor $6.715$
Analytic rank $0$
Dimension $48$
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 = [48,-4,-6,-6,1] 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: \(48\)
Relative dimension: \(8\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 4 q^{2} - 6 q^{3} - 6 q^{4} + q^{5} - 3 q^{6} - 15 q^{8} - 8 q^{9} + 3 q^{10} - 5 q^{11} + 72 q^{12} + 4 q^{13} - 15 q^{14} + 7 q^{15} + 2 q^{16} + 54 q^{17} + 11 q^{18} - 17 q^{19} + 7 q^{20} - 25 q^{21}+ \cdots + 90 q^{99}+O(q^{100}) \) 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 −2.26970 − 1.09303i 0.654995 − 0.821338i 2.70986 + 3.39805i 1.32042 + 0.635882i −2.38439 + 1.14826i 2.57292 − 3.22635i −1.31525 − 5.76249i 0.421985 + 1.84884i −2.30193 − 2.88653i
190.2 −2.15716 − 1.03884i 1.31018 − 1.64292i 2.32720 + 2.91821i 2.18748 + 1.05344i −4.53300 + 2.18298i −0.235910 + 0.295821i −0.923050 − 4.04415i −0.315036 − 1.38026i −3.62441 − 4.54487i
190.3 −1.73762 − 0.836795i 0.302293 − 0.379063i 1.07213 + 1.34441i −2.65771 − 1.27989i −0.842470 + 0.405712i 1.62444 − 2.03699i 0.120353 + 0.527303i 0.615255 + 2.69561i 3.54710 + 4.44792i
190.4 −0.938760 − 0.452083i −1.34483 + 1.68636i −0.570088 − 0.714867i −1.31745 − 0.634453i 2.02485 − 0.975115i −2.36982 + 2.97166i 0.675706 + 2.96046i −0.367688 − 1.61095i 0.949949 + 1.19120i
190.5 0.0377915 + 0.0181994i 1.88776 − 2.36718i −1.24588 − 1.56229i 1.56952 + 0.755841i 0.114422 − 0.0551030i 1.28043 − 1.60561i −0.0373185 − 0.163503i −1.37232 − 6.01254i 0.0455587 + 0.0571287i
190.6 0.836654 + 0.402911i −1.02888 + 1.29017i −0.709327 − 0.889468i 0.454733 + 0.218988i −1.38064 + 0.664881i −2.58918 + 3.24673i −0.648358 − 2.84064i 0.0616082 + 0.269923i 0.292221 + 0.366434i
190.7 1.25619 + 0.604951i 0.0173539 − 0.0217611i −0.0349213 − 0.0437899i 1.03288 + 0.497407i 0.0349642 − 0.0168379i −0.0688706 + 0.0863610i −0.637886 − 2.79476i 0.667390 + 2.92403i 0.996587 + 1.24968i
190.8 1.36873 + 0.659148i 1.94206 − 2.43527i 0.191979 + 0.240734i −1.68890 − 0.813330i 4.26336 − 2.05313i −0.214022 + 0.268375i −0.572010 − 2.50614i −1.49136 − 6.53408i −1.77555 − 2.22647i
571.1 −2.26970 + 1.09303i 0.654995 + 0.821338i 2.70986 − 3.39805i 1.32042 − 0.635882i −2.38439 − 1.14826i 2.57292 + 3.22635i −1.31525 + 5.76249i 0.421985 − 1.84884i −2.30193 + 2.88653i
571.2 −2.15716 + 1.03884i 1.31018 + 1.64292i 2.32720 − 2.91821i 2.18748 − 1.05344i −4.53300 − 2.18298i −0.235910 − 0.295821i −0.923050 + 4.04415i −0.315036 + 1.38026i −3.62441 + 4.54487i
571.3 −1.73762 + 0.836795i 0.302293 + 0.379063i 1.07213 − 1.34441i −2.65771 + 1.27989i −0.842470 − 0.405712i 1.62444 + 2.03699i 0.120353 − 0.527303i 0.615255 − 2.69561i 3.54710 − 4.44792i
571.4 −0.938760 + 0.452083i −1.34483 − 1.68636i −0.570088 + 0.714867i −1.31745 + 0.634453i 2.02485 + 0.975115i −2.36982 − 2.97166i 0.675706 − 2.96046i −0.367688 + 1.61095i 0.949949 − 1.19120i
571.5 0.0377915 − 0.0181994i 1.88776 + 2.36718i −1.24588 + 1.56229i 1.56952 − 0.755841i 0.114422 + 0.0551030i 1.28043 + 1.60561i −0.0373185 + 0.163503i −1.37232 + 6.01254i 0.0455587 − 0.0571287i
571.6 0.836654 − 0.402911i −1.02888 − 1.29017i −0.709327 + 0.889468i 0.454733 − 0.218988i −1.38064 − 0.664881i −2.58918 − 3.24673i −0.648358 + 2.84064i 0.0616082 − 0.269923i 0.292221 − 0.366434i
571.7 1.25619 − 0.604951i 0.0173539 + 0.0217611i −0.0349213 + 0.0437899i 1.03288 − 0.497407i 0.0349642 + 0.0168379i −0.0688706 − 0.0863610i −0.637886 + 2.79476i 0.667390 − 2.92403i 0.996587 − 1.24968i
571.8 1.36873 − 0.659148i 1.94206 + 2.43527i 0.191979 − 0.240734i −1.68890 + 0.813330i 4.26336 + 2.05313i −0.214022 − 0.268375i −0.572010 + 2.50614i −1.49136 + 6.53408i −1.77555 + 2.22647i
574.1 −0.947194 + 1.18774i −0.693113 + 3.03673i −0.0685165 − 0.300190i 1.16875 − 1.46557i −2.95034 − 3.69961i 0.0763836 − 0.334658i −2.31602 − 1.11534i −6.03839 − 2.90794i 0.633686 + 2.77636i
574.2 −0.869314 + 1.09008i −0.00619353 + 0.0271356i 0.0124633 + 0.0546051i −0.714773 + 0.896297i −0.0241960 − 0.0303408i 0.0245796 − 0.107690i −2.58275 − 1.24379i 2.70221 + 1.30132i −0.355678 − 1.55833i
574.3 −0.578982 + 0.726021i 0.367202 − 1.60882i 0.253156 + 1.10915i −0.314685 + 0.394602i 0.955433 + 1.19807i 0.924068 − 4.04861i −2.62515 − 1.26420i 0.249447 + 0.120127i −0.104293 − 0.456936i
574.4 −0.0261525 + 0.0327942i −0.673734 + 2.95182i 0.444650 + 1.94814i −1.08614 + 1.36198i −0.0791828 − 0.0992921i −0.456981 + 2.00217i −0.151099 − 0.0727657i −5.55642 − 2.67583i −0.0162597 − 0.0712384i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 190.8
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.p 48
29.b even 2 1 841.2.d.q 48
29.c odd 4 2 841.2.e.m 96
29.d even 7 1 841.2.a.j yes 8
29.d even 7 5 inner 841.2.d.p 48
29.e even 14 1 841.2.a.i ✓ 8
29.e even 14 5 841.2.d.q 48
29.f odd 28 2 841.2.b.f 16
29.f odd 28 10 841.2.e.m 96
87.h odd 14 1 7569.2.a.bi 8
87.j odd 14 1 7569.2.a.bd 8
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
841.2.a.i ✓ 8 29.e even 14 1
841.2.a.j yes 8 29.d even 7 1
841.2.b.f 16 29.f odd 28 2
841.2.d.p 48 1.a even 1 1 trivial
841.2.d.p 48 29.d even 7 5 inner
841.2.d.q 48 29.b even 2 1
841.2.d.q 48 29.e even 14 5
841.2.e.m 96 29.c odd 4 2
841.2.e.m 96 29.f odd 28 10
7569.2.a.bd 8 87.j odd 14 1
7569.2.a.bi 8 87.h odd 14 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{48} + 4 T_{2}^{47} + 19 T_{2}^{46} + 65 T_{2}^{45} + 225 T_{2}^{44} + 701 T_{2}^{43} + 2154 T_{2}^{42} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(841, [\chi])\). Copy content Toggle raw display