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Properties

Label 31734.2.a.bf
Level $31734$
Weight $2$
Character orbit 31734.a
Self dual yes
Analytic conductor $253.397$
Dimension $16$

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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] = [31734,2,Mod(1,31734)] 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("31734.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31734, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 31734 = 2 \cdot 3^{2} \cdot 41 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 31734.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,-16,0,16,13,0,-4,-16,0,-13,4,0,-12,4,0,16,12,0,-1,13,0,-4, 8,0,13,12,0,-4,6,0,7,-16,0,-12,20,0,21,1,0,-13,16,0,16,4,0,-8,-2,0,18, -13,0,-12,23,0,-2,4,0,-6,31,0,8,-7,0,16,19,0,-16,12,0,-20,13,0,-28,-21, 0,-1,48,0,45,13,0,-16,19,0,12,-16,0,-4,40,0,-15,8,0,2,-12,0,-56,-18,0, 13] 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: \(253.397265774\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} - 37 x^{14} + 88 x^{13} + 539 x^{12} - 998 x^{11} - 3901 x^{10} + 5599 x^{9} + \cdots + 256 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 16 q - 16 q^{2} + 16 q^{4} + 13 q^{5} - 4 q^{7} - 16 q^{8} - 13 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 16 q^{16} + 12 q^{17} - q^{19} + 13 q^{20} - 4 q^{22} + 8 q^{23} + 13 q^{25} + 12 q^{26} - 4 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(41\) \( -1 \)
\(43\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.