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Properties

Label 2790.2.e.b
Level $2790$
Weight $2$
Character orbit 2790.e
Analytic conductor $22.278$
Analytic rank $0$
Dimension $32$
Inner twists $4$

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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] = [2790,2,Mod(2789,2790)] 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("2790.2789"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2790, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32,32] 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: \(22.2782621639\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 32 q^{2} + 32 q^{4} + 4 q^{5} + 32 q^{8} + 4 q^{10} + 32 q^{16} - 16 q^{19} + 4 q^{20} + 4 q^{25} + 32 q^{32} + 8 q^{35} - 16 q^{38} + 4 q^{40} - 8 q^{47} - 24 q^{49} + 4 q^{50} + 32 q^{64} + 8 q^{70}+ \cdots - 24 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2789.1 1.00000 0 1.00000 −2.22926 − 0.174304i 0 − 0.535781i 1.00000 0 −2.22926 − 0.174304i
2789.2 1.00000 0 1.00000 −2.22926 − 0.174304i 0 − 0.535781i 1.00000 0 −2.22926 − 0.174304i
2789.3 1.00000 0 1.00000 −2.22926 + 0.174304i 0 0.535781i 1.00000 0 −2.22926 + 0.174304i
2789.4 1.00000 0 1.00000 −2.22926 + 0.174304i 0 0.535781i 1.00000 0 −2.22926 + 0.174304i
2789.5 1.00000 0 1.00000 −1.43349 − 1.71613i 0 − 0.897988i 1.00000 0 −1.43349 − 1.71613i
2789.6 1.00000 0 1.00000 −1.43349 − 1.71613i 0 − 0.897988i 1.00000 0 −1.43349 − 1.71613i
2789.7 1.00000 0 1.00000 −1.43349 + 1.71613i 0 0.897988i 1.00000 0 −1.43349 + 1.71613i
2789.8 1.00000 0 1.00000 −1.43349 + 1.71613i 0 0.897988i 1.00000 0 −1.43349 + 1.71613i
2789.9 1.00000 0 1.00000 −1.18560 − 1.89588i 0 3.81363i 1.00000 0 −1.18560 − 1.89588i
2789.10 1.00000 0 1.00000 −1.18560 − 1.89588i 0 3.81363i 1.00000 0 −1.18560 − 1.89588i
2789.11 1.00000 0 1.00000 −1.18560 + 1.89588i 0 − 3.81363i 1.00000 0 −1.18560 + 1.89588i
2789.12 1.00000 0 1.00000 −1.18560 + 1.89588i 0 − 3.81363i 1.00000 0 −1.18560 + 1.89588i
2789.13 1.00000 0 1.00000 −0.432401 − 2.19386i 0 − 2.88146i 1.00000 0 −0.432401 − 2.19386i
2789.14 1.00000 0 1.00000 −0.432401 − 2.19386i 0 − 2.88146i 1.00000 0 −0.432401 − 2.19386i
2789.15 1.00000 0 1.00000 −0.432401 + 2.19386i 0 2.88146i 1.00000 0 −0.432401 + 2.19386i
2789.16 1.00000 0 1.00000 −0.432401 + 2.19386i 0 2.88146i 1.00000 0 −0.432401 + 2.19386i
2789.17 1.00000 0 1.00000 0.360590 − 2.20680i 0 1.81961i 1.00000 0 0.360590 − 2.20680i
2789.18 1.00000 0 1.00000 0.360590 − 2.20680i 0 1.81961i 1.00000 0 0.360590 − 2.20680i
2789.19 1.00000 0 1.00000 0.360590 + 2.20680i 0 − 1.81961i 1.00000 0 0.360590 + 2.20680i
2789.20 1.00000 0 1.00000 0.360590 + 2.20680i 0 − 1.81961i 1.00000 0 0.360590 + 2.20680i
See all 32 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 2789.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
15.d odd 2 1 inner
31.b odd 2 1 inner
465.g even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2790.2.e.b yes 32
3.b odd 2 1 2790.2.e.a ✓ 32
5.b even 2 1 2790.2.e.a ✓ 32
15.d odd 2 1 inner 2790.2.e.b yes 32
31.b odd 2 1 inner 2790.2.e.b yes 32
93.c even 2 1 2790.2.e.a ✓ 32
155.c odd 2 1 2790.2.e.a ✓ 32
465.g even 2 1 inner 2790.2.e.b yes 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2790.2.e.a ✓ 32 3.b odd 2 1
2790.2.e.a ✓ 32 5.b even 2 1
2790.2.e.a ✓ 32 93.c even 2 1
2790.2.e.a ✓ 32 155.c odd 2 1
2790.2.e.b yes 32 1.a even 1 1 trivial
2790.2.e.b yes 32 15.d odd 2 1 inner
2790.2.e.b yes 32 31.b odd 2 1 inner
2790.2.e.b yes 32 465.g even 2 1 inner