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Properties

Label 627.2.j.d
Level $627$
Weight $2$
Character orbit 627.j
Analytic conductor $5.007$
Analytic rank $0$
Dimension $48$
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] = [627,2,Mod(58,627)] 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("627.58"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 627 = 3 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 627.j (of order \(5\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.00662020673\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 3 q^{2} - 12 q^{3} - 21 q^{4} - 2 q^{5} + 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} + 2 q^{10} - 15 q^{11} + 74 q^{12} + 4 q^{13} - 24 q^{14} - 7 q^{15} - 25 q^{16} + 11 q^{17} - 2 q^{18} + 12 q^{19}+ \cdots - 5 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
58.1 −2.11187 + 1.53436i 0.309017 + 0.951057i 1.48769 − 4.57863i 3.35778 + 2.43957i −2.11187 − 1.53436i −0.926090 + 2.85021i 2.27016 + 6.98682i −0.809017 + 0.587785i −10.8344
58.2 −2.06226 + 1.49832i 0.309017 + 0.951057i 1.38992 − 4.27772i −0.615292 − 0.447036i −2.06226 − 1.49832i 0.660018 − 2.03133i 1.96760 + 6.05565i −0.809017 + 0.587785i 1.93869
58.3 −1.72493 + 1.25324i 0.309017 + 0.951057i 0.786754 − 2.42138i −3.42790 − 2.49052i −1.72493 − 1.25324i −0.479654 + 1.47622i 0.359733 + 1.10714i −0.809017 + 0.587785i 9.03410
58.4 −0.782102 + 0.568230i 0.309017 + 0.951057i −0.329236 + 1.01328i −0.534189 − 0.388111i −0.782102 − 0.568230i −1.56670 + 4.82180i −0.915756 − 2.81841i −0.809017 + 0.587785i 0.638327
58.5 −0.588622 + 0.427659i 0.309017 + 0.951057i −0.454450 + 1.39865i −1.02019 − 0.741209i −0.588622 − 0.427659i 1.29179 − 3.97571i −0.780315 − 2.40156i −0.809017 + 0.587785i 0.917489
58.6 0.0657473 − 0.0477682i 0.309017 + 0.951057i −0.615993 + 1.89583i 2.17188 + 1.57796i 0.0657473 + 0.0477682i −0.568000 + 1.74812i 0.100287 + 0.308652i −0.809017 + 0.587785i 0.218171
58.7 0.265896 − 0.193185i 0.309017 + 0.951057i −0.584654 + 1.79938i −2.23293 − 1.62232i 0.265896 + 0.193185i 0.858966 − 2.64363i 0.395282 + 1.21655i −0.809017 + 0.587785i −0.907136
58.8 1.19604 − 0.868977i 0.309017 + 0.951057i 0.0573668 − 0.176557i −2.18819 − 1.58981i 1.19604 + 0.868977i −0.569713 + 1.75340i 0.828886 + 2.55105i −0.809017 + 0.587785i −3.99868
58.9 1.24506 − 0.904586i 0.309017 + 0.951057i 0.113854 − 0.350407i 2.86588 + 2.08219i 1.24506 + 0.904586i 1.51688 − 4.66849i 0.775919 + 2.38803i −0.809017 + 0.587785i 5.45170
58.10 1.65003 − 1.19882i 0.309017 + 0.951057i 0.667400 − 2.05405i 0.548371 + 0.398415i 1.65003 + 1.19882i −0.906984 + 2.79141i −0.100685 − 0.309877i −0.809017 + 0.587785i 1.38245
58.11 1.96889 − 1.43048i 0.309017 + 0.951057i 1.21222 − 3.73082i −3.27684 − 2.38076i 1.96889 + 1.43048i −0.0301523 + 0.0927992i −1.44606 − 4.45051i −0.809017 + 0.587785i −9.85739
58.12 2.18714 − 1.58905i 0.309017 + 0.951057i 1.64046 − 5.04881i 1.61555 + 1.17377i 2.18714 + 1.58905i 0.601600 − 1.85153i −2.76407 − 8.50693i −0.809017 + 0.587785i 5.39861
115.1 −0.851316 − 2.62008i −0.809017 − 0.587785i −4.52205 + 3.28546i 0.837122 − 2.57640i −0.851316 + 2.62008i −3.77984 + 2.74621i 8.00032 + 5.81257i 0.309017 + 0.951057i −7.46302
115.2 −0.826496 − 2.54369i −0.809017 − 0.587785i −4.16924 + 3.02913i −0.160039 + 0.492550i −0.826496 + 2.54369i 3.38338 − 2.45817i 6.82344 + 4.95752i 0.309017 + 0.951057i 1.38517
115.3 −0.500247 − 1.53960i −0.809017 − 0.587785i −0.502094 + 0.364792i −1.05148 + 3.23611i −0.500247 + 1.53960i 3.47743 − 2.52650i −1.80652 − 1.31251i 0.309017 + 0.951057i 5.50832
115.4 −0.471765 − 1.45194i −0.809017 − 0.587785i −0.267543 + 0.194382i 1.03061 − 3.17190i −0.471765 + 1.45194i 0.872292 − 0.633757i −2.06174 − 1.49795i 0.309017 + 0.951057i −5.09162
115.5 −0.393256 − 1.21032i −0.809017 − 0.587785i 0.307812 − 0.223639i −0.120480 + 0.370799i −0.393256 + 1.21032i −2.45110 + 1.78083i −2.45084 − 1.78064i 0.309017 + 0.951057i 0.496164
115.6 −0.0802465 − 0.246973i −0.809017 − 0.587785i 1.56348 − 1.13593i −0.402758 + 1.23956i −0.0802465 + 0.246973i 1.27421 − 0.925771i −0.826185 − 0.600259i 0.309017 + 0.951057i 0.338459
115.7 0.243519 + 0.749473i −0.809017 − 0.587785i 1.11563 − 0.810549i 1.25975 − 3.87712i 0.243519 − 0.749473i 2.54451 − 1.84870i 2.15424 + 1.56515i 0.309017 + 0.951057i 3.21257
115.8 0.285641 + 0.879113i −0.809017 − 0.587785i 0.926786 − 0.673349i 0.275964 − 0.849330i 0.285641 − 0.879113i −1.05275 + 0.764867i 2.35231 + 1.70906i 0.309017 + 0.951057i 0.825483
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 58.12
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 627.2.j.d ✓ 48
11.c even 5 1 inner 627.2.j.d ✓ 48
11.c even 5 1 6897.2.a.bp 24
11.d odd 10 1 6897.2.a.bq 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
627.2.j.d ✓ 48 1.a even 1 1 trivial
627.2.j.d ✓ 48 11.c even 5 1 inner
6897.2.a.bp 24 11.c even 5 1
6897.2.a.bq 24 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{48} - 3 T_{2}^{47} + 27 T_{2}^{46} - 71 T_{2}^{45} + 409 T_{2}^{44} - 984 T_{2}^{43} + \cdots + 774400 \) acting on \(S_{2}^{\mathrm{new}}(627, [\chi])\). Copy content Toggle raw display