Properties

Label 2912.2.h.a
Level 29122912
Weight 22
Character orbit 2912.h
Analytic conductor 23.25223.252
Analytic rank 00
Dimension 4848
Inner twists 22

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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] = [2912,2,Mod(2575,2912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2912, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) 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("2912.2575"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2912=25713 2912 = 2^{5} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2912.h (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,0,0,0,0,0,0,0,-48,0,4,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 23.252437068623.2524370686
Analytic rank: 00
Dimension: 4848
Twist minimal: no (minimal twist has level 728)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

qq-expansion

The algebraic qq-expansion of this newform has not been computed, but we have computed the trace expansion.

Tr(f)(q)=\operatorname{Tr}(f)(q) = 48q48q9+4q1148q13+48q2512q35+4q43+24q45+40q5120q63+4q6720q77+64q81+40q8720q99+O(q100) 48 q - 48 q^{9} + 4 q^{11} - 48 q^{13} + 48 q^{25} - 12 q^{35} + 4 q^{43} + 24 q^{45} + 40 q^{51} - 20 q^{63} + 4 q^{67} - 20 q^{77} + 64 q^{81} + 40 q^{87} - 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\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   a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
2575.1 0 3.37415i 0 −0.523773 0 2.30913 1.29148i 0 −8.38487 0
2575.2 0 3.10974i 0 3.50914 0 1.29016 2.30987i 0 −6.67047 0
2575.3 0 3.06517i 0 −4.00290 0 −1.79836 1.94059i 0 −6.39524 0
2575.4 0 3.03518i 0 −0.163903 0 −0.919188 + 2.48095i 0 −6.21234 0
2575.5 0 2.89173i 0 −2.33723 0 1.68858 + 2.03684i 0 −5.36210 0
2575.6 0 2.65471i 0 −0.263032 0 2.63919 + 0.186171i 0 −4.04746 0
2575.7 0 2.44281i 0 3.85137 0 −2.49284 + 0.886436i 0 −2.96733 0
2575.8 0 2.38356i 0 −1.68057 0 −1.10198 2.40533i 0 −2.68138 0
2575.9 0 2.32841i 0 2.37629 0 −2.43296 1.03956i 0 −2.42149 0
2575.10 0 2.21460i 0 1.27531 0 −0.643326 + 2.56635i 0 −1.90445 0
2575.11 0 1.92788i 0 −2.16680 0 −1.74001 + 1.99308i 0 −0.716713 0
2575.12 0 1.61368i 0 −3.74465 0 −0.220320 + 2.63656i 0 0.396033 0
2575.13 0 1.53313i 0 0.856056 0 −1.33356 2.28509i 0 0.649528 0
2575.14 0 1.48862i 0 1.02997 0 1.70779 2.02076i 0 0.784007 0
2575.15 0 1.40360i 0 −3.11493 0 2.64532 0.0479799i 0 1.02989 0
2575.16 0 1.35635i 0 2.01767 0 2.18534 + 1.49140i 0 1.16033 0
2575.17 0 1.31268i 0 2.82361 0 −0.786324 + 2.52620i 0 1.27686 0
2575.18 0 0.913695i 0 −3.26760 0 0.184260 2.63933i 0 2.16516 0
2575.19 0 0.788146i 0 −0.604005 0 2.57195 + 0.620533i 0 2.37883 0
2575.20 0 0.742757i 0 2.66467 0 −2.25806 1.37882i 0 2.44831 0
See all 48 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2575.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
56.e even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2912.2.h.a 48
4.b odd 2 1 728.2.h.a 48
7.b odd 2 1 2912.2.h.b 48
8.b even 2 1 728.2.h.b yes 48
8.d odd 2 1 2912.2.h.b 48
28.d even 2 1 728.2.h.b yes 48
56.e even 2 1 inner 2912.2.h.a 48
56.h odd 2 1 728.2.h.a 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
728.2.h.a 48 4.b odd 2 1
728.2.h.a 48 56.h odd 2 1
728.2.h.b yes 48 8.b even 2 1
728.2.h.b yes 48 28.d even 2 1
2912.2.h.a 48 1.a even 1 1 trivial
2912.2.h.a 48 56.e even 2 1 inner
2912.2.h.b 48 7.b odd 2 1
2912.2.h.b 48 8.d odd 2 1