↑

Properties

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

Related objects

Downloads

Learn more

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,-12,0,12,7,0,-5,-12,0,-7,11,0,-9,5,0,12,1,0,-7,7,0,-11,-12, 0,17,9,0,-5,18,0,-17,-12,0,-1,-28,0,-31,7,0,-7,-6,0,0,11,0,12,-28,0,-7, -17,0,-9,13,0,14,5,0,-18,-34,0,22,17,0,12,63,0,-23,1,0,28,52,0,22,31,0, -7,19,0,-15,7,0,6,-14,0,-7,0,0,-11,61,0,0,-12,0,28,-14,0,-41,7,0,17] 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: \( x^{12} - 3 x^{11} - 20 x^{10} + 56 x^{9} + 146 x^{8} - 389 x^{7} - 463 x^{6} + 1249 x^{5} + 566 x^{4} + \cdots - 251 \) 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.

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