↑

Properties

Label 29640.2.a.bg
Level $29640$
Weight $2$
Character orbit 29640.a
Self dual yes
Analytic conductor $236.677$
Dimension $10$
CM no
Inner twists $1$

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] = [29640,2,Mod(1,29640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29640, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("29640.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 29640 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29640.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [10,0,10,0,10,0,-3,0,10,0,-6,0,10,0,10,0,-7,0,10,0,-3,0,-9,0, 10,0,10,0,-21,0,-11,0,-6,0,-3,0,-23,0,10,0,-11,0,-11,0,10,0,-18,0,-19, 0,-7,0,-7,0,-6,0,10,0,1,0,-16,0,-3,0,10,0,-9,0,-9,0,-18,0,-21,0,10,0,-25, 0,-39,0,10,0,-14,0,-7,0,-21,0,-9,0,-3,0,-11,0,10,0,-33,0,-6,0] 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: \(236.676591591\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3x^{9} - 21x^{8} + 63x^{7} + 127x^{6} - 322x^{5} - 430x^{4} + 499x^{3} + 728x^{2} + 154x + 4 \) Copy content Toggle raw display
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q + 10 q^{3} + 10 q^{5} - 3 q^{7} + 10 q^{9} - 6 q^{11} + 10 q^{13} + 10 q^{15} - 7 q^{17} + 10 q^{19} - 3 q^{21} - 9 q^{23} + 10 q^{25} + 10 q^{27} - 21 q^{29} - 11 q^{31} - 6 q^{33} - 3 q^{35} - 23 q^{37}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(13\) \( -1 \)
\(19\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.