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Properties

Label 33282.2.a.dy
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
Dimension $20$

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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 = [20,20,0,20,6,0,-20,20,0,6,2,0,-2,-20,0,20,-8,0,-28,6,0,2,0,0, 24,-2,0,-20,24,0,-14,20,0,-8,-30,0,-42,-28,0,6,-30,0,0,2,0,0,28,0,30,24, 0,-2,-8,0,-48,-20,0,24,-28,0,8,-14,0,20,-36,0,4,-8,0,-30,38,0,-92,-42, 0,-28,2,0,8,6,0,-30,-30,0,-52,0,0,2,-20,0,-38,0,0,28,74,0,-34,30,0,24] 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: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 10 x^{19} + 4 x^{18} + 238 x^{17} - 487 x^{16} - 2314 x^{15} + 6521 x^{14} + 11932 x^{13} + \cdots + 2377 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 20 q + 20 q^{2} + 20 q^{4} + 6 q^{5} - 20 q^{7} + 20 q^{8} + 6 q^{10} + 2 q^{11} - 2 q^{13} - 20 q^{14} + 20 q^{16} - 8 q^{17} - 28 q^{19} + 6 q^{20} + 2 q^{22} + 24 q^{25} - 2 q^{26} - 20 q^{28} + 24 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) \) 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.