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Properties

Label 11900.2.a.bd
Level $11900$
Weight $2$
Character orbit 11900.a
Self dual yes
Analytic conductor $95.022$
Dimension $10$

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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 = [10,0,-2,0,0,0,-10,0,20,0,-2,0,-12,0,0,0,10,0,12,0,2,0,-12,0, 0,0,-2,0,-2,0,24,0,-14,0,0,0,8,0,12,0,6,0,16,0,0,0,0,0,10,0,-2,0,-6,0, 0,0,-32,0,28,0,14,0,-20,0,0,0,-18,0,8,0,8,0,-10,0,0,0,2,0,46,0,10,0,-8, 0,0,0,18,0,-16,0,12,0,-4,0,0,0,-28,0,20,0] 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: \(10\)
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: \( x^{10} - 2x^{9} - 23x^{8} + 44x^{7} + 180x^{6} - 332x^{5} - 552x^{4} + 966x^{3} + 562x^{2} - 758x - 265 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q - 2 q^{3} - 10 q^{7} + 20 q^{9} - 2 q^{11} - 12 q^{13} + 10 q^{17} + 12 q^{19} + 2 q^{21} - 12 q^{23} - 2 q^{27} - 2 q^{29} + 24 q^{31} - 14 q^{33} + 8 q^{37} + 12 q^{39} + 6 q^{41} + 16 q^{43} + 10 q^{49}+ \cdots + 20 q^{99}+O(q^{100}) \) 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.