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Properties

Label 19275.2.a.r
Level $19275$
Weight $2$
Character orbit 19275.a
Self dual yes
Analytic conductor $153.912$
Dimension $42$

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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] = [19275,2,Mod(1,19275)] 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("19275.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 19275 = 3 \cdot 5^{2} \cdot 257 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19275.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [42,-4,42,40,0,-4,-13,-18,42,0,-19,40,-31,-2,0,44,-30,-4,6,0, -13,-18,-16,-18,0,-19,42,-36,-25,0,0,-45,-19,-14,0,40,-47,-27,-31,0,-8, -2,-34,-45,0,-10,-20,44,43,0,-30,-56,-42,-4,0,-3,6,-15,-15,0,-6,-37,-13, 38,0,-18,-33,-77,-16,0,-27,-18,-54,-44,0,32,-77,-19,-9,0,42,-75,-29,-36, 0,-20,-25,-1,-10,0,6,-89,0,24,0,-45,-73,-26,-19,0] 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: \(153.911649896\)
Dimension: \(42\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 42 q - 4 q^{2} + 42 q^{3} + 40 q^{4} - 4 q^{6} - 13 q^{7} - 18 q^{8} + 42 q^{9} - 19 q^{11} + 40 q^{12} - 31 q^{13} - 2 q^{14} + 44 q^{16} - 30 q^{17} - 4 q^{18} + 6 q^{19} - 13 q^{21} - 18 q^{22} - 16 q^{23}+ \cdots - 19 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( +1 \)
\(257\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.