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Properties

Label 11900.2.a.n
Level $11900$
Weight $2$
Character orbit 11900.a
Self dual yes
Analytic conductor $95.022$
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] = [11900,2,Mod(1,11900)] 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("11900.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11900, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 11900 = 2^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 11900.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,0,0,0,0,-3,0,-3,0,-3,0,-3,0,0,0,3,0,-3,0,0,0,9,0,0,0,-3, 0,-3,0,3,0,12,0,0,0,6,0,-3,0,-3,0,-3,0,0,0,9,0,3,0,0,0,9,0,0,0,0,0,-21, 0,-3,0,3,0,0,0,3,0,0,0,-9,0,3,0,0,0,3,0,-12,0,-9,0,6,0,0,0,3,0,-3,0,3, 0,21,0,0,0,-6,0,-3,0] 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: \(95.0219784053\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{18})^+\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 3x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{7} - 3 q^{9} - 3 q^{11} - 3 q^{13} + 3 q^{17} - 3 q^{19} + 9 q^{23} - 3 q^{27} - 3 q^{29} + 3 q^{31} + 12 q^{33} + 6 q^{37} - 3 q^{39} - 3 q^{41} - 3 q^{43} + 9 q^{47} + 3 q^{49} + 9 q^{53} - 21 q^{59}+ \cdots - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(7\) \( +1 \)
\(17\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.