Properties

Label 5184.2.c.b
Level $5184$
Weight $2$
Character orbit 5184.c
Analytic conductor $41.394$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-3}) \)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{6}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + ( 1 - 2 \zeta_{6} ) q^{5} + ( 1 - 2 \zeta_{6} ) q^{7} +O(q^{10})\) \( q + ( 1 - 2 \zeta_{6} ) q^{5} + ( 1 - 2 \zeta_{6} ) q^{7} -3 q^{11} + 5 q^{13} + ( 4 - 8 \zeta_{6} ) q^{17} + ( -2 + 4 \zeta_{6} ) q^{19} + 9 q^{23} + 2 q^{25} + ( -1 + 2 \zeta_{6} ) q^{29} + ( -3 + 6 \zeta_{6} ) q^{31} -3 q^{35} -2 q^{37} + ( 3 - 6 \zeta_{6} ) q^{41} + ( 3 - 6 \zeta_{6} ) q^{43} + 3 q^{47} + 4 q^{49} + ( -3 + 6 \zeta_{6} ) q^{55} + 3 q^{59} + q^{61} + ( 5 - 10 \zeta_{6} ) q^{65} + ( -5 + 10 \zeta_{6} ) q^{67} + 12 q^{71} -2 q^{73} + ( -3 + 6 \zeta_{6} ) q^{77} + ( 5 - 10 \zeta_{6} ) q^{79} -15 q^{83} -12 q^{85} + ( -4 + 8 \zeta_{6} ) q^{89} + ( 5 - 10 \zeta_{6} ) q^{91} + 6 q^{95} -5 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + O(q^{10}) \) \( 2q - 6q^{11} + 10q^{13} + 18q^{23} + 4q^{25} - 6q^{35} - 4q^{37} + 6q^{47} + 8q^{49} + 6q^{59} + 2q^{61} + 24q^{71} - 4q^{73} - 30q^{83} - 24q^{85} + 12q^{95} - 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5183.1
0.500000 + 0.866025i
0.500000 0.866025i
0 0 0 1.73205i 0 1.73205i 0 0 0
5183.2 0 0 0 1.73205i 0 1.73205i 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
12.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5184.2.c.b 2
3.b odd 2 1 5184.2.c.d 2
4.b odd 2 1 5184.2.c.d 2
8.b even 2 1 1296.2.c.c 2
8.d odd 2 1 1296.2.c.a 2
9.c even 3 1 576.2.s.c 2
9.c even 3 1 1728.2.s.c 2
9.d odd 6 1 576.2.s.b 2
9.d odd 6 1 1728.2.s.d 2
12.b even 2 1 inner 5184.2.c.b 2
24.f even 2 1 1296.2.c.c 2
24.h odd 2 1 1296.2.c.a 2
36.f odd 6 1 576.2.s.b 2
36.f odd 6 1 1728.2.s.d 2
36.h even 6 1 576.2.s.c 2
36.h even 6 1 1728.2.s.c 2
72.j odd 6 1 144.2.s.b 2
72.j odd 6 1 432.2.s.b 2
72.l even 6 1 144.2.s.c yes 2
72.l even 6 1 432.2.s.a 2
72.n even 6 1 144.2.s.c yes 2
72.n even 6 1 432.2.s.a 2
72.p odd 6 1 144.2.s.b 2
72.p odd 6 1 432.2.s.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
144.2.s.b 2 72.j odd 6 1
144.2.s.b 2 72.p odd 6 1
144.2.s.c yes 2 72.l even 6 1
144.2.s.c yes 2 72.n even 6 1
432.2.s.a 2 72.l even 6 1
432.2.s.a 2 72.n even 6 1
432.2.s.b 2 72.j odd 6 1
432.2.s.b 2 72.p odd 6 1
576.2.s.b 2 9.d odd 6 1
576.2.s.b 2 36.f odd 6 1
576.2.s.c 2 9.c even 3 1
576.2.s.c 2 36.h even 6 1
1296.2.c.a 2 8.d odd 2 1
1296.2.c.a 2 24.h odd 2 1
1296.2.c.c 2 8.b even 2 1
1296.2.c.c 2 24.f even 2 1
1728.2.s.c 2 9.c even 3 1
1728.2.s.c 2 36.h even 6 1
1728.2.s.d 2 9.d odd 6 1
1728.2.s.d 2 36.f odd 6 1
5184.2.c.b 2 1.a even 1 1 trivial
5184.2.c.b 2 12.b even 2 1 inner
5184.2.c.d 2 3.b odd 2 1
5184.2.c.d 2 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5184, [\chi])\):

\( T_{5}^{2} + 3 \)
\( T_{7}^{2} + 3 \)
\( T_{11} + 3 \)