↑

Properties

Label 19275.2.a.o
Level $19275$
Weight $2$
Character orbit 19275.a
Self dual yes
Analytic conductor $153.912$
Dimension $28$

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] = [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 = [28,-7,-28,35,0,7,-20,-18,28,0,12,-35,-35,7,0,45,-14,-7,24,0, 20,-6,-5,18,0,-4,-28,-38,17,0,15,-28,-12,2,0,35,-44,15,35,0,32,-7,-41, 8,0,-9,-4,-45,54,0,14,-47,-12,7,0,-12,-24,-10,-5,0,4,6,-20,18,0,6,-29, 14,5,0,7,-18,-73,10,0,1,-8,4,11,0,28,-6,19,38,0,-26,-17,-19,-3,0,24,-12, -15,-3,0,28,-66,42,12,0] 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: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 7 q^{2} - 28 q^{3} + 35 q^{4} + 7 q^{6} - 20 q^{7} - 18 q^{8} + 28 q^{9} + 12 q^{11} - 35 q^{12} - 35 q^{13} + 7 q^{14} + 45 q^{16} - 14 q^{17} - 7 q^{18} + 24 q^{19} + 20 q^{21} - 6 q^{22} - 5 q^{23}+ \cdots + 12 q^{99}+O(q^{100}) \) 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.