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Properties

Label 48552.2.a.cq
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 = [6,0,6,0,0,0,6,0,6,0,0,0,5,0,0,0,0,0,1,0,6,0,5,0,14,0,6,0,0,0, 7,0,0,0,0,0,0,0,5,0,5,0,-6,0,0,0,8,0,6,0,0,0,-2,0,5,0,1,0,-3,0,-1,0,6, 0,-9,0,-15,0,5,0,12,0,7,0,14,0,0,0,-6,0,6,0,14,0,0,0,0,0,11,0,5,0,7,0, 17,0,19,0,0,0] 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: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 20x^{4} + 31x^{3} + 52x^{2} - 78x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q + 6 q^{3} + 6 q^{7} + 6 q^{9} + 5 q^{13} + q^{19} + 6 q^{21} + 5 q^{23} + 14 q^{25} + 6 q^{27} + 7 q^{31} + 5 q^{39} + 5 q^{41} - 6 q^{43} + 8 q^{47} + 6 q^{49} - 2 q^{53} + 5 q^{55} + q^{57} - 3 q^{59}+ \cdots + 19 q^{97}+O(q^{100}) \) 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.