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Properties

Label 33282.2.a.dc
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
Dimension $10$

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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 = [10,-10,0,10,10,0,-10,-10,0,-10,14,0,-10,10,0,10,-2,0,-10,10, 0,-14,-22,0,-18,10,0,-10,10,0,-16,-10,0,2,-10,0,8,10,0,-10,18,0,0,14,0, 22,14,0,-16,18,0,-10,22,0,14,10,0,-10,4,0,10,16,0,10,12,0,-24,-2,0,10, 58,0,-24,-8,0,-10,8,0,-40,10,0,-18,2,0,-2,0,0,-14,10,0,10,-22,0,-14,12, 0,-26,16,0,-18] 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: \(10\)
Coefficient field: \(\Q(\zeta_{44})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q - 10 q^{2} + 10 q^{4} + 10 q^{5} - 10 q^{7} - 10 q^{8} - 10 q^{10} + 14 q^{11} - 10 q^{13} + 10 q^{14} + 10 q^{16} - 2 q^{17} - 10 q^{19} + 10 q^{20} - 14 q^{22} - 22 q^{23} - 18 q^{25} + 10 q^{26}+ \cdots + 16 q^{98}+O(q^{100}) \) 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.