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Properties

Label 19275.2.a.n
Level $19275$
Weight $2$
Character orbit 19275.a
Self dual yes
Analytic conductor $153.912$
Dimension $25$

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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 = [25,-4,25,26,0,-4,10,-9,25,0,18,26,13,17,0,24,0,-4,-12,0,10,6, -1,-9,0,12,25,10,29,0,-9,-27,18,0,0,26,18,-7,13,0,54,17,13,72,0,13,-2, 24,35,0,0,25,-14,-4,0,56,-12,-4,33,0,-8,2,10,33,0,6,19,-4,-1,0,49,-9,23, 82,0,-29,10,12,7,0,25,-2,-3,10,0,58,29,-19,37,0,-20,-54,-9,15,0,-27,-6, -61,18,0] 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: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 4 q^{2} + 25 q^{3} + 26 q^{4} - 4 q^{6} + 10 q^{7} - 9 q^{8} + 25 q^{9} + 18 q^{11} + 26 q^{12} + 13 q^{13} + 17 q^{14} + 24 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{21} + 6 q^{22} - q^{23} - 9 q^{24}+ \cdots + 18 q^{99}+O(q^{100}) \) 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.