↑

Properties

Label 24200.2.a.em
Level $24200$
Weight $2$
Character orbit 24200.a
Self dual yes
Analytic conductor $193.238$
Dimension $18$

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] = [24200,2,Mod(1,24200)] 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("24200.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 24200 = 2^{3} \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 24200.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [18,0,-4,0,0,0,-1,0,18,0,0,0,-1,0,0,0,-2,0,-11,0,8,0,-15,0,0, 0,-28,0,12,0,0,0,0,0,0,0,-17,0,-4,0,13,0,-10,0,0,0,-21,0,21,0,-24,0,-11, 0,0,0,14,0,7,0,12,0,-7,0,0,0,-32,0,-8,0,-10,0,48,0,0,0,0,0,-6,0,22,0,-32, 0,0,0,-2,0,-1,0,22,0,-62,0,0,0,-34,0,0,0] 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: \(193.237972891\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 4 x^{17} - 28 x^{16} + 116 x^{15} + 313 x^{14} - 1362 x^{13} - 1723 x^{12} + 8274 x^{11} + \cdots + 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 18 q - 4 q^{3} - q^{7} + 18 q^{9} - q^{13} - 2 q^{17} - 11 q^{19} + 8 q^{21} - 15 q^{23} - 28 q^{27} + 12 q^{29} - 17 q^{37} - 4 q^{39} + 13 q^{41} - 10 q^{43} - 21 q^{47} + 21 q^{49} - 24 q^{51} - 11 q^{53}+ \cdots - 34 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.