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Properties

Label 19663.2.a.l
Level $19663$
Weight $2$
Character orbit 19663.a
Self dual yes
Analytic conductor $157.010$
Dimension $13$

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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] = [19663,2,Mod(1,19663)] 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("19663.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19663, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 19663 = 7 \cdot 53^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19663.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [13,1,5,13,4,4,-13,6,12,2,-1,17,-1,-1,18,17,5,-24,-10,36,-5,-8, 5,10,11,-8,38,-13,0,-1,7,13,20,-19,-4,45,-1,-17,23,3,11,-4,11,10,12,-20, 9,107,13,8,-19,18,0,15,22,-6,-7,22,15,109,0,-81,-12,30,1,-56,15,-26,-32, -2,-8,2,17,17,10,51,1,-28,-30,65,65,-7,10,-17,7,-1,-4,-27,-15,-12,1,-27, -26,-36,-5,14,7,1,-16,13] 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: \(157.009845494\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - x^{12} - 19 x^{11} + 16 x^{10} + 134 x^{9} - 90 x^{8} - 437 x^{7} + 214 x^{6} + 666 x^{5} + \cdots - 7 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 13 q + q^{2} + 5 q^{3} + 13 q^{4} + 4 q^{5} + 4 q^{6} - 13 q^{7} + 6 q^{8} + 12 q^{9} + 2 q^{10} - q^{11} + 17 q^{12} - q^{13} - q^{14} + 18 q^{15} + 17 q^{16} + 5 q^{17} - 24 q^{18} - 10 q^{19} + 36 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(53\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.