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Properties

Label 48552.2.a.dc
Level $48552$
Weight $2$
Character orbit 48552.a
Self dual yes
Analytic conductor $387.690$
Dimension $18$

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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 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);
 
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")
 
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 = [18,0,-18,0,-6,0,18,0,18,0,0,0,-12,0,6,0,0,0,-3,0,-18,0,6,0,12, 0,-18,0,0,0,15,0,0,0,-6,0,-21,0,12,0,-15,0,-6,0,-6,0,-15,0,18,0,0,0,18, 0,-30,0,3,0,-21,0,-21,0,18,0,-3,0,30,0,-6,0,15,0,-24,0,-12,0,0,0,27,0, 18,0,18,0,0,0,0,0,30,0,-12,0,-15,0,24,0,-12,0,0,0] 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: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 6 x^{17} - 33 x^{16} + 235 x^{15} + 345 x^{14} - 3516 x^{13} - 411 x^{12} + 24894 x^{11} + \cdots + 8 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 18 q - 18 q^{3} - 6 q^{5} + 18 q^{7} + 18 q^{9} - 12 q^{13} + 6 q^{15} - 3 q^{19} - 18 q^{21} + 6 q^{23} + 12 q^{25} - 18 q^{27} + 15 q^{31} - 6 q^{35} - 21 q^{37} + 12 q^{39} - 15 q^{41} - 6 q^{43} - 6 q^{45}+ \cdots - 12 q^{97}+O(q^{100}) \) 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.