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Properties

Label 48552.2.a.cn
Level $48552$
Weight $2$
Character orbit 48552.a
Self dual yes
Analytic conductor $387.690$
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] = [48552,2,Mod(1,48552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48552.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 48552 = 2^{3} \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48552.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,6,0,-2,0,6,0,6,0,0,0,1,0,-2,0,0,0,-5,0,6,0,3,0,-2,0,6,0, -6,0,13,0,0,0,-2,0,-6,0,1,0,-9,0,-4,0,-2,0,-14,0,6,0,0,0,-4,0,-17,0,-5, 0,-3,0,-7,0,6,0,-5,0,-1,0,3,0,-6,0,-13,0,-2,0,0,0,16,0,6,0,-2,0,0,0,-6, 0,-21,0,1,0,13,0,-1,0,3,0,0,0] 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: \(387.689671894\)
Dimension: \(6\)
Coefficient field: 6.6.346669661.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 12x^{4} + 11x^{3} + 47x^{2} + 7x - 24 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q + 6 q^{3} - 2 q^{5} + 6 q^{7} + 6 q^{9} + q^{13} - 2 q^{15} - 5 q^{19} + 6 q^{21} + 3 q^{23} - 2 q^{25} + 6 q^{27} - 6 q^{29} + 13 q^{31} - 2 q^{35} - 6 q^{37} + q^{39} - 9 q^{41} - 4 q^{43} - 2 q^{45}+ \cdots + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.