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Properties

Label 783.2.v.b
Level $783$
Weight $2$
Character orbit 783.v
Analytic conductor $6.252$
Analytic rank $0$
Dimension $240$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [783,2,Mod(26,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 19])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.26"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 783 = 3^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 783.v (of order \(28\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [240,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.25228647827\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(20\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240 q + 72 q^{16} + 8 q^{19} - 40 q^{25} + 8 q^{31} - 32 q^{37} - 16 q^{40} - 16 q^{43} - 104 q^{46} - 8 q^{49} + 8 q^{52} - 128 q^{55} + 272 q^{58} - 24 q^{61} + 112 q^{67} - 56 q^{70} - 64 q^{73} - 160 q^{76}+ \cdots + 40 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
26.1 −2.29631 − 1.44287i 0 2.32340 + 4.82460i 0.235496 + 1.03178i 0 −0.0740862 − 0.0356780i 1.01870 − 9.04125i 0 0.947943 − 2.70907i
26.2 −2.07110 − 1.30136i 0 1.72815 + 3.58855i −0.163082 − 0.714507i 0 3.59907 + 1.73322i 0.543074 − 4.81991i 0 −0.592072 + 1.69204i
26.3 −1.88722 − 1.18582i 0 1.28767 + 2.67387i 0.811731 + 3.55642i 0 −3.00488 − 1.44708i 0.241509 − 2.14345i 0 2.68536 − 7.67433i
26.4 −1.74225 − 1.09473i 0 0.969232 + 2.01263i −0.919748 − 4.02968i 0 1.28939 + 0.620939i 0.0538749 − 0.478153i 0 −2.80897 + 8.02757i
26.5 −1.41984 − 0.892143i 0 0.352252 + 0.731460i −0.199609 − 0.874544i 0 −0.0690112 − 0.0332341i −0.223072 + 1.97982i 0 −0.496806 + 1.41979i
26.6 −1.35702 − 0.852674i 0 0.246690 + 0.512256i 0.285749 + 1.25195i 0 0.725362 + 0.349316i −0.256861 + 2.27970i 0 0.679736 − 1.94257i
26.7 −0.756163 − 0.475129i 0 −0.521732 − 1.08339i −0.476790 − 2.08895i 0 −2.48263 − 1.19557i −0.320213 + 2.84197i 0 −0.631991 + 1.80613i
26.8 −0.631385 − 0.396725i 0 −0.626512 − 1.30097i −0.272604 − 1.19435i 0 2.74133 + 1.32015i −0.287535 + 2.55194i 0 −0.301713 + 0.862245i
26.9 −0.561561 − 0.352852i 0 −0.676921 − 1.40564i 0.901677 + 3.95051i 0 3.71421 + 1.78867i −0.264364 + 2.34630i 0 0.887598 − 2.53661i
26.10 −0.453334 − 0.284849i 0 −0.743394 − 1.54367i 0.606168 + 2.65580i 0 −2.92524 − 1.40872i −0.222599 + 1.97562i 0 0.481704 − 1.37663i
26.11 0.453334 + 0.284849i 0 −0.743394 − 1.54367i −0.606168 − 2.65580i 0 −2.92524 − 1.40872i 0.222599 − 1.97562i 0 0.481704 − 1.37663i
26.12 0.561561 + 0.352852i 0 −0.676921 − 1.40564i −0.901677 − 3.95051i 0 3.71421 + 1.78867i 0.264364 − 2.34630i 0 0.887598 − 2.53661i
26.13 0.631385 + 0.396725i 0 −0.626512 − 1.30097i 0.272604 + 1.19435i 0 2.74133 + 1.32015i 0.287535 − 2.55194i 0 −0.301713 + 0.862245i
26.14 0.756163 + 0.475129i 0 −0.521732 − 1.08339i 0.476790 + 2.08895i 0 −2.48263 − 1.19557i 0.320213 − 2.84197i 0 −0.631991 + 1.80613i
26.15 1.35702 + 0.852674i 0 0.246690 + 0.512256i −0.285749 − 1.25195i 0 0.725362 + 0.349316i 0.256861 − 2.27970i 0 0.679736 − 1.94257i
26.16 1.41984 + 0.892143i 0 0.352252 + 0.731460i 0.199609 + 0.874544i 0 −0.0690112 − 0.0332341i 0.223072 − 1.97982i 0 −0.496806 + 1.41979i
26.17 1.74225 + 1.09473i 0 0.969232 + 2.01263i 0.919748 + 4.02968i 0 1.28939 + 0.620939i −0.0538749 + 0.478153i 0 −2.80897 + 8.02757i
26.18 1.88722 + 1.18582i 0 1.28767 + 2.67387i −0.811731 − 3.55642i 0 −3.00488 − 1.44708i −0.241509 + 2.14345i 0 2.68536 − 7.67433i
26.19 2.07110 + 1.30136i 0 1.72815 + 3.58855i 0.163082 + 0.714507i 0 3.59907 + 1.73322i −0.543074 + 4.81991i 0 −0.592072 + 1.69204i
26.20 2.29631 + 1.44287i 0 2.32340 + 4.82460i −0.235496 − 1.03178i 0 −0.0740862 − 0.0356780i −1.01870 + 9.04125i 0 0.947943 − 2.70907i
See next 80 embeddings (of 240 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 26.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
29.f odd 28 1 inner
87.k even 28 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 783.2.v.b ✓ 240
3.b odd 2 1 inner 783.2.v.b ✓ 240
29.f odd 28 1 inner 783.2.v.b ✓ 240
87.k even 28 1 inner 783.2.v.b ✓ 240
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
783.2.v.b ✓ 240 1.a even 1 1 trivial
783.2.v.b ✓ 240 3.b odd 2 1 inner
783.2.v.b ✓ 240 29.f odd 28 1 inner
783.2.v.b ✓ 240 87.k even 28 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{240} - 158 T_{2}^{236} + 13877 T_{2}^{232} + 784 T_{2}^{230} - 986490 T_{2}^{228} + \cdots + 28\!\cdots\!61 \) acting on \(S_{2}^{\mathrm{new}}(783, [\chi])\). Copy content Toggle raw display