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Properties

Label 31433.2.a.z
Level $31433$
Weight $2$
Character orbit 31433.a
Self dual yes
Analytic conductor $250.994$
Dimension $174$

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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 = [174,13,30,169,25,-8,71,36,166,4,0,76,2,5,37,167,174,86,52,-28, -1,117,5,-28,123,20,126,143,94,9,3,90,33,13,13,129,82,-48,103,15,11,28, 0,-61,76,2,-34,204,195,39,30,-98,-10,103,148,94,9,39,18,50,77,101,160, 140,126,112,-59,169,61,72,204,227,126,112,154,96,45,92,-10,-62,162,76, 2,74,25,0,-39,241,-33,17,201,4,140,-216,-59,-32,-18,82,20,117] 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: \(174\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 174 q + 13 q^{2} + 30 q^{3} + 169 q^{4} + 25 q^{5} - 8 q^{6} + 71 q^{7} + 36 q^{8} + 166 q^{9} + 4 q^{10} + 76 q^{12} + 2 q^{13} + 5 q^{14} + 37 q^{15} + 167 q^{16} + 174 q^{17} + 86 q^{18} + 52 q^{19}+ \cdots + 20 q^{99}+O(q^{100}) \) 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.