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Properties

Label 18032.2.a.dq
Level $18032$
Weight $2$
Character orbit 18032.a
Self dual yes
Analytic conductor $143.986$
Dimension $11$

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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] = [18032,2,Mod(1,18032)] 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("18032.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18032, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 18032 = 2^{4} \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18032.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [11,0,-4,0,3,0,0,0,11,0,0,0,-13,0,0,0,7,0,-8,0,0,0,11,0,6,0,-25, 0,-3,0,-12,0,-2,0,0,0,-1,0,21,0,12,0,-9,0,19,0,-17,0,0,0,-19,0,-5,0,-21, 0,11,0,-33,0,-15,0,0,0,-9,0,5,0,-4,0,9,0,5,0,-44,0,0,0,-11,0,-13,0,-51, 0,33,0,-4,0,26,0,0,0,6,0,19,0,21,0,-15,0] 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: \(143.986244925\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 4 x^{10} - 14 x^{9} + 61 x^{8} + 71 x^{7} - 343 x^{6} - 152 x^{5} + 867 x^{4} + 102 x^{3} + \cdots + 243 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 11 q - 4 q^{3} + 3 q^{5} + 11 q^{9} - 13 q^{13} + 7 q^{17} - 8 q^{19} + 11 q^{23} + 6 q^{25} - 25 q^{27} - 3 q^{29} - 12 q^{31} - 2 q^{33} - q^{37} + 21 q^{39} + 12 q^{41} - 9 q^{43} + 19 q^{45} - 17 q^{47}+ \cdots - 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(7\) \( -1 \)
\(23\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.