↑

Properties

Label 19275.2.a.l
Level $19275$
Weight $2$
Character orbit 19275.a
Self dual yes
Analytic conductor $153.912$
Dimension $17$

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 = [17,7,17,17,0,7,0,24,17,0,4,17,17,-7,0,17,26,7,6,0,0,8,17,24, 0,8,17,2,-11,0,3,40,4,10,0,17,18,19,17,0,-36,-7,13,-4,0,7,32,17,5,0,26, 29,42,7,0,-26,6,28,3,0,-16,34,0,26,0,8,9,39,17,0,-7,24,41,12,0,7,48,8, -1,0,17,0,43,2,0,-6,-11,7,-7,0,8,44,3,51,0,40,42,49,4,0] 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: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{17} - 7 x^{16} - x^{15} + 104 x^{14} - 142 x^{13} - 569 x^{12} + 1198 x^{11} + 1374 x^{10} + \cdots + 97 \) 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.

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