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Properties

Label 17298.2.a.cy
Level $17298$
Weight $2$
Character orbit 17298.a
Self dual yes
Analytic conductor $138.125$
Dimension $4$

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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] = [17298,2,Mod(1,17298)] 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("17298.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17298, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17298 = 2 \cdot 3^{2} \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17298.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,4,0,4,7,0,1,4,0,7,-3,0,10,1,0,4,7,0,-8,7,0,-3,15,0,1,10,0, 1,9,0,0,4,0,7,-7,0,18,-8,0,7,8,0,0,-3,0,15,-2,0,11,1,0,10,21,0,-19,1,0, 9,-3,0,-15,0,0,4,25,0,-27,7,0,-7,22,0,7,18,0,-8,28,0,9,7,0,8,14,0,21,0, 0,-3,4,0,10,15,0,-2,-24,0,-17,11,0,1] 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: \(138.125225416\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{15})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 4 q^{2} + 4 q^{4} + 7 q^{5} + q^{7} + 4 q^{8} + 7 q^{10} - 3 q^{11} + 10 q^{13} + q^{14} + 4 q^{16} + 7 q^{17} - 8 q^{19} + 7 q^{20} - 3 q^{22} + 15 q^{23} + q^{25} + 10 q^{26} + q^{28} + 9 q^{29}+ \cdots + 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(31\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.