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Properties

Label 16830.2.a.du
Level $16830$
Weight $2$
Character orbit 16830.a
Self dual yes
Analytic conductor $134.388$
Dimension $3$

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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] = [16830,2,Mod(1,16830)] 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("16830.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16830, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16830 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16830.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,0,3,-3,0,-2,-3,0,3,-3,0,-3,2,0,3,3,0,15,-3,0,3,-2,0,3,3, 0,-2,-7,0,10,-3,0,-3,2,0,3,-15,0,3,18,0,1,-3,0,2,-10,0,21,-3,0,-3,-16, 0,3,2,0,7,-2,0,-19,-10,0,3,3,0,-9,3,0,-2,24,0,8,-3,0,15,2,0,8,-3,0,-18, -9,0,-3,-1,0,3,0,0,-17,-2,0,10,-15,0,4,-21,0,3] 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: \(134.388226602\)
Dimension: \(3\)
Coefficient field: 3.3.2089.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 13x - 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} - 3 q^{8} + 3 q^{10} - 3 q^{11} - 3 q^{13} + 2 q^{14} + 3 q^{16} + 3 q^{17} + 15 q^{19} - 3 q^{20} + 3 q^{22} - 2 q^{23} + 3 q^{25} + 3 q^{26} - 2 q^{28} - 7 q^{29}+ \cdots - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(11\) \( +1 \)
\(17\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.