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Properties

Label 33282.2.a.cy
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
Dimension $9$

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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 = [9,9,0,9,2,0,4,9,0,2,-3,0,7,4,0,9,-16,0,12,2,0,-3,3,0,35,7,0, 4,20,0,2,9,0,-16,15,0,-1,12,0,2,8,0,0,-3,0,3,-27,0,39,35,0,7,8,0,-1,4, 0,20,24,0,-23,2,0,9,-2,0,34,-16,0,15,-14,0,18,-1,0,12,21,0,-8,2,0,8,9, 0,-7,0,0,-3,31,0,29,3,0,-27,-58,0,37,39,0,35] 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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - x^{8} - 21x^{7} + 21x^{6} + 139x^{5} - 134x^{4} - 299x^{3} + 225x^{2} + 137x - 41 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 9 q + 9 q^{2} + 9 q^{4} + 2 q^{5} + 4 q^{7} + 9 q^{8} + 2 q^{10} - 3 q^{11} + 7 q^{13} + 4 q^{14} + 9 q^{16} - 16 q^{17} + 12 q^{19} + 2 q^{20} - 3 q^{22} + 3 q^{23} + 35 q^{25} + 7 q^{26} + 4 q^{28} + 20 q^{29}+ \cdots + 39 q^{98}+O(q^{100}) \) 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.