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Properties

Label 273.4.i.d
Level $273$
Weight $4$
Character orbit 273.i
Analytic conductor $16.108$
Analytic rank $0$
Dimension $22$
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] = [273,4,Mod(79,273)] 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("273.79"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22,1] 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: \(16.1075214316\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q + q^{2} + 33 q^{3} - 31 q^{4} - 17 q^{5} + 6 q^{6} + 11 q^{7} - 108 q^{8} - 99 q^{9} - 75 q^{10} - 7 q^{11} + 93 q^{12} - 286 q^{13} + 141 q^{14} - 102 q^{15} - 23 q^{16} + 20 q^{17} + 9 q^{18} - 242 q^{19}+ \cdots + 126 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
79.1 −2.41866 + 4.18924i 1.50000 + 2.59808i −7.69985 − 13.3365i −8.18902 + 14.1838i −14.5120 −17.0779 − 7.16557i 35.7947 −4.50000 + 7.79423i −39.6129 − 68.6116i
79.2 −1.90344 + 3.29686i 1.50000 + 2.59808i −3.24618 − 5.62255i 1.56078 − 2.70335i −11.4206 18.3193 + 2.72123i −5.73941 −4.50000 + 7.79423i 5.94170 + 10.2913i
79.3 −1.58042 + 2.73736i 1.50000 + 2.59808i −0.995443 − 1.72416i 5.41386 − 9.37707i −9.48251 −12.6948 − 13.4848i −18.9938 −4.50000 + 7.79423i 17.1123 + 29.6394i
79.4 −0.983292 + 1.70311i 1.50000 + 2.59808i 2.06628 + 3.57889i −5.15341 + 8.92597i −5.89975 7.75355 − 16.8191i −23.8597 −4.50000 + 7.79423i −10.1346 − 17.5537i
79.5 −0.688131 + 1.19188i 1.50000 + 2.59808i 3.05295 + 5.28787i −9.34357 + 16.1835i −4.12879 17.1515 + 6.98767i −19.4134 −4.50000 + 7.79423i −12.8592 − 22.2728i
79.6 −0.307232 + 0.532142i 1.50000 + 2.59808i 3.81122 + 6.60122i 4.74528 − 8.21906i −1.84339 0.718632 + 18.5063i −9.59944 −4.50000 + 7.79423i 2.91581 + 5.05032i
79.7 0.839829 − 1.45463i 1.50000 + 2.59808i 2.58938 + 4.48493i −5.32469 + 9.22263i 5.03897 −0.881446 + 18.4993i 22.1358 −4.50000 + 7.79423i 8.94366 + 15.4909i
79.8 1.23012 − 2.13063i 1.50000 + 2.59808i 0.973597 + 1.68632i 10.5453 − 18.2649i 7.38074 8.18155 − 16.6151i 24.4725 −4.50000 + 7.79423i −25.9439 − 44.9362i
79.9 1.46556 − 2.53843i 1.50000 + 2.59808i −0.295738 − 0.512233i −0.172304 + 0.298440i 8.79337 −18.5090 − 0.646308i 21.7153 −4.50000 + 7.79423i 0.505045 + 0.874763i
79.10 2.16028 − 3.74171i 1.50000 + 2.59808i −5.33359 − 9.23804i 1.67947 − 2.90893i 12.9617 16.4106 − 8.58437i −11.5237 −4.50000 + 7.79423i −7.25625 − 12.5682i
79.11 2.68539 − 4.65123i 1.50000 + 2.59808i −10.4226 − 18.0525i −4.26165 + 7.38139i 16.1123 −13.8719 + 12.2707i −68.9889 −4.50000 + 7.79423i 22.8884 + 39.6438i
235.1 −2.41866 − 4.18924i 1.50000 − 2.59808i −7.69985 + 13.3365i −8.18902 − 14.1838i −14.5120 −17.0779 + 7.16557i 35.7947 −4.50000 − 7.79423i −39.6129 + 68.6116i
235.2 −1.90344 − 3.29686i 1.50000 − 2.59808i −3.24618 + 5.62255i 1.56078 + 2.70335i −11.4206 18.3193 − 2.72123i −5.73941 −4.50000 − 7.79423i 5.94170 − 10.2913i
235.3 −1.58042 − 2.73736i 1.50000 − 2.59808i −0.995443 + 1.72416i 5.41386 + 9.37707i −9.48251 −12.6948 + 13.4848i −18.9938 −4.50000 − 7.79423i 17.1123 − 29.6394i
235.4 −0.983292 − 1.70311i 1.50000 − 2.59808i 2.06628 − 3.57889i −5.15341 − 8.92597i −5.89975 7.75355 + 16.8191i −23.8597 −4.50000 − 7.79423i −10.1346 + 17.5537i
235.5 −0.688131 − 1.19188i 1.50000 − 2.59808i 3.05295 − 5.28787i −9.34357 − 16.1835i −4.12879 17.1515 − 6.98767i −19.4134 −4.50000 − 7.79423i −12.8592 + 22.2728i
235.6 −0.307232 − 0.532142i 1.50000 − 2.59808i 3.81122 − 6.60122i 4.74528 + 8.21906i −1.84339 0.718632 − 18.5063i −9.59944 −4.50000 − 7.79423i 2.91581 − 5.05032i
235.7 0.839829 + 1.45463i 1.50000 − 2.59808i 2.58938 − 4.48493i −5.32469 − 9.22263i 5.03897 −0.881446 − 18.4993i 22.1358 −4.50000 − 7.79423i 8.94366 − 15.4909i
235.8 1.23012 + 2.13063i 1.50000 − 2.59808i 0.973597 − 1.68632i 10.5453 + 18.2649i 7.38074 8.18155 + 16.6151i 24.4725 −4.50000 − 7.79423i −25.9439 + 44.9362i
235.9 1.46556 + 2.53843i 1.50000 − 2.59808i −0.295738 + 0.512233i −0.172304 − 0.298440i 8.79337 −18.5090 + 0.646308i 21.7153 −4.50000 − 7.79423i 0.505045 − 0.874763i
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 79.11
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 273.4.i.d ✓ 22
7.c even 3 1 inner 273.4.i.d ✓ 22
7.c even 3 1 1911.4.a.v 11
7.d odd 6 1 1911.4.a.w 11
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
273.4.i.d ✓ 22 1.a even 1 1 trivial
273.4.i.d ✓ 22 7.c even 3 1 inner
1911.4.a.v 11 7.c even 3 1
1911.4.a.w 11 7.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{22} - T_{2}^{21} + 60 T_{2}^{20} - 13 T_{2}^{19} + 2297 T_{2}^{18} - 23 T_{2}^{17} + \cdots + 740275264 \) acting on \(S_{4}^{\mathrm{new}}(273, [\chi])\). Copy content Toggle raw display