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Properties

Label 33282.2.a.dr
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
Dimension $15$

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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 = [15,-15,0,15,11,0,1,-15,0,-11,-1,0,-20,-1,0,15,2,0,-4,11,0,1, 0,0,2,20,0,1,9,0,-11,-15,0,-2,-8,0,-6,4,0,-11,-8,0,0,-1,0,0,22,0,-2,-2, 0,-20,-1,0,-7,-1,0,-9,23,0,28,11,0,15,-16,0,-16,2,0,8,26,0,-3,6,0,-4,12, 0,-13,11,0,8,-13,0,-20,0,0,1,0,0,60,0,0,-22,-102,0,-11,2,0,2] 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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 4 x^{14} - 27 x^{13} + 109 x^{12} + 262 x^{11} - 1078 x^{10} - 1081 x^{9} + 4713 x^{8} + \cdots + 23 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 15 q - 15 q^{2} + 15 q^{4} + 11 q^{5} + q^{7} - 15 q^{8} - 11 q^{10} - q^{11} - 20 q^{13} - q^{14} + 15 q^{16} + 2 q^{17} - 4 q^{19} + 11 q^{20} + q^{22} + 2 q^{25} + 20 q^{26} + q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) \) 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.