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Properties

Label 10368.2.a.ck
Level $10368$
Weight $2$
Character orbit 10368.a
Self dual yes
Analytic conductor $82.789$
Dimension $6$

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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] = [10368,2,Mod(1,10368)] 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("10368.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10368, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10368 = 2^{7} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10368.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,0,0,4,0,0,0,0,0,4,0,-2,0,0,0,-8,0,4,0,0,0,8,0,4,0,0,0,4, 0,-4,0,0,0,-4,0,-6,0,0,0,-8,0,-8,0,0,0,16,0,6,0,0,0,24,0,20,0,0,0,24,0, 2,0,0,0,-8,0,4,0,0,0,8,0,6,0,0,0,8,0,4,0,0,0,24,0,-2,0,0,0,-24,0,-4,0, 0,0,16,0,4,0,0,0] 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: \(82.7888968157\)
Dimension: \(6\)
Coefficient field: 6.6.31083264.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 10x^{4} + 10x^{3} + 32x^{2} - 8x - 26 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q + 4 q^{5} + 4 q^{11} - 2 q^{13} - 8 q^{17} + 4 q^{19} + 8 q^{23} + 4 q^{25} + 4 q^{29} - 4 q^{31} - 4 q^{35} - 6 q^{37} - 8 q^{41} - 8 q^{43} + 16 q^{47} + 6 q^{49} + 24 q^{53} + 20 q^{55} + 24 q^{59}+ \cdots + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.