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Properties

Label 17400.2.a.df
Level $17400$
Weight $2$
Character orbit 17400.a
Self dual yes
Analytic conductor $138.940$
Dimension $11$

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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] = [17400,2,Mod(1,17400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17400, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17400.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 17400 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17400.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [11,0,-11,0,0,0,0,0,11,0,1,0,-14,0,0,0,-4,0,-6,0,0,0,-3,0,0,0, -11,0,-11,0,-10,0,-1,0,0,0,-31,0,14,0,9,0,1,0,0,0,-8,0,13,0,4,0,-19,0, 0,0,6,0,8,0,16,0,0,0,0,0,6,0,3,0,26,0,-27,0,0,0,-36,0,16,0,11,0,17,0,0, 0,11,0,-22,0,44,0,10,0,0,0,-37,0,1,0] 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: \(138.939699517\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 3x^{10} - 18x^{9} + 60x^{8} + 67x^{7} - 281x^{6} - 65x^{5} + 445x^{4} + 30x^{3} - 226x^{2} - 35x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 11 q - 11 q^{3} + 11 q^{9} + q^{11} - 14 q^{13} - 4 q^{17} - 6 q^{19} - 3 q^{23} - 11 q^{27} - 11 q^{29} - 10 q^{31} - q^{33} - 31 q^{37} + 14 q^{39} + 9 q^{41} + q^{43} - 8 q^{47} + 13 q^{49} + 4 q^{51}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(29\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.