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Properties

Label 31433.2.a.r
Level $31433$
Weight $2$
Character orbit 31433.a
Self dual yes
Analytic conductor $250.994$
Dimension $90$

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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] = [31433,2,Mod(1,31433)] 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("31433.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31433, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 31433 = 17 \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 31433.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [90,7,6,95,-1,3,27,21,96,-4,2,16,-6,5,-19,97,-90,28,28,93,0,35, -1,-3,63,14,18,63,2,6,-10,54,30,-7,7,112,92,30,20,-17,4,29,0,67,-43,-1, 35,6,87,35,-6,52,-17,84,76,43,1,-24,0,-260,20,-3,161,103,-16,66,-48,-95, 52,6,10,96,51,14,26,46,15,44,-6,111,90,31,1,62,1,0,39,28,-3,21,58,-14, 71,226,63,66,12,60,9,87] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(250.993768673\)
Dimension: \(90\)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 90 q + 7 q^{2} + 6 q^{3} + 95 q^{4} - q^{5} + 3 q^{6} + 27 q^{7} + 21 q^{8} + 96 q^{9} - 4 q^{10} + 2 q^{11} + 16 q^{12} - 6 q^{13} + 5 q^{14} - 19 q^{15} + 97 q^{16} - 90 q^{17} + 28 q^{18} + 28 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(17\) \( +1 \)
\(43\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.