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Properties

Label 33282.2.a.dh
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
Dimension $12$

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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] = [33282,2,Mod(1,33282)] 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("33282.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33282, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33282 = 2 \cdot 3^{2} \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33282.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,-12,0,12,-9,0,7,-12,0,9,7,0,-5,-7,0,12,11,0,1,-9,0,-7,-10, 0,41,5,0,7,-36,0,1,-12,0,-11,-24,0,11,-1,0,9,14,0,0,7,0,10,4,0,13,-41, 0,-5,35,0,60,-7,0,36,2,0,-40,-1,0,12,7,0,5,11,0,24,-44,0,2,-11,0,1,13, 0,29,-9,0,-14,2,0,29,0,0,-7,-31,0,32,-10,0,-4,-26,0,-5,-13,0,41] 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: \(265.758108007\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} - 26 x^{10} + 111 x^{9} + 214 x^{8} - 1087 x^{7} - 510 x^{6} + 4571 x^{5} + \cdots - 2009 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q - 12 q^{2} + 12 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8} + 9 q^{10} + 7 q^{11} - 5 q^{13} - 7 q^{14} + 12 q^{16} + 11 q^{17} + q^{19} - 9 q^{20} - 7 q^{22} - 10 q^{23} + 41 q^{25} + 5 q^{26} + 7 q^{28}+ \cdots - 13 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(43\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.