Properties

Label 6084.2.a.i
Level $6084$
Weight $2$
Character orbit 6084.a
Self dual yes
Analytic conductor $48.581$
Analytic rank $0$
Dimension $1$
CM discriminant -3
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6084 = 2^{2} \cdot 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6084.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.5809845897\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 36)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q + 4 q^{7} + O(q^{10}) \) \( q + 4 q^{7} - 8 q^{19} - 5 q^{25} + 4 q^{31} + 10 q^{37} + 8 q^{43} + 9 q^{49} + 14 q^{61} + 16 q^{67} + 10 q^{73} - 4 q^{79} - 14 q^{97} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 0 0 0 0 4.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(13\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6084.2.a.i 1
3.b odd 2 1 CM 6084.2.a.i 1
13.b even 2 1 36.2.a.a 1
13.d odd 4 2 6084.2.b.f 2
39.d odd 2 1 36.2.a.a 1
39.f even 4 2 6084.2.b.f 2
52.b odd 2 1 144.2.a.a 1
65.d even 2 1 900.2.a.g 1
65.h odd 4 2 900.2.d.b 2
91.b odd 2 1 1764.2.a.e 1
91.r even 6 2 1764.2.k.h 2
91.s odd 6 2 1764.2.k.g 2
104.e even 2 1 576.2.a.e 1
104.h odd 2 1 576.2.a.f 1
117.n odd 6 2 324.2.e.c 2
117.t even 6 2 324.2.e.c 2
143.d odd 2 1 4356.2.a.g 1
156.h even 2 1 144.2.a.a 1
195.e odd 2 1 900.2.a.g 1
195.s even 4 2 900.2.d.b 2
208.o odd 4 2 2304.2.d.a 2
208.p even 4 2 2304.2.d.q 2
260.g odd 2 1 3600.2.a.e 1
260.p even 4 2 3600.2.f.m 2
273.g even 2 1 1764.2.a.e 1
273.w odd 6 2 1764.2.k.h 2
273.ba even 6 2 1764.2.k.g 2
312.b odd 2 1 576.2.a.e 1
312.h even 2 1 576.2.a.f 1
364.h even 2 1 7056.2.a.bb 1
429.e even 2 1 4356.2.a.g 1
468.x even 6 2 1296.2.i.h 2
468.bg odd 6 2 1296.2.i.h 2
624.v even 4 2 2304.2.d.a 2
624.bi odd 4 2 2304.2.d.q 2
780.d even 2 1 3600.2.a.e 1
780.w odd 4 2 3600.2.f.m 2
1092.d odd 2 1 7056.2.a.bb 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
36.2.a.a 1 13.b even 2 1
36.2.a.a 1 39.d odd 2 1
144.2.a.a 1 52.b odd 2 1
144.2.a.a 1 156.h even 2 1
324.2.e.c 2 117.n odd 6 2
324.2.e.c 2 117.t even 6 2
576.2.a.e 1 104.e even 2 1
576.2.a.e 1 312.b odd 2 1
576.2.a.f 1 104.h odd 2 1
576.2.a.f 1 312.h even 2 1
900.2.a.g 1 65.d even 2 1
900.2.a.g 1 195.e odd 2 1
900.2.d.b 2 65.h odd 4 2
900.2.d.b 2 195.s even 4 2
1296.2.i.h 2 468.x even 6 2
1296.2.i.h 2 468.bg odd 6 2
1764.2.a.e 1 91.b odd 2 1
1764.2.a.e 1 273.g even 2 1
1764.2.k.g 2 91.s odd 6 2
1764.2.k.g 2 273.ba even 6 2
1764.2.k.h 2 91.r even 6 2
1764.2.k.h 2 273.w odd 6 2
2304.2.d.a 2 208.o odd 4 2
2304.2.d.a 2 624.v even 4 2
2304.2.d.q 2 208.p even 4 2
2304.2.d.q 2 624.bi odd 4 2
3600.2.a.e 1 260.g odd 2 1
3600.2.a.e 1 780.d even 2 1
3600.2.f.m 2 260.p even 4 2
3600.2.f.m 2 780.w odd 4 2
4356.2.a.g 1 143.d odd 2 1
4356.2.a.g 1 429.e even 2 1
6084.2.a.i 1 1.a even 1 1 trivial
6084.2.a.i 1 3.b odd 2 1 CM
6084.2.b.f 2 13.d odd 4 2
6084.2.b.f 2 39.f even 4 2
7056.2.a.bb 1 364.h even 2 1
7056.2.a.bb 1 1092.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6084))\):

\( T_{5} \)
\( T_{7} - 4 \)
\( T_{11} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -4 + T \)
$11$ \( T \)
$13$ \( T \)
$17$ \( T \)
$19$ \( 8 + T \)
$23$ \( T \)
$29$ \( T \)
$31$ \( -4 + T \)
$37$ \( -10 + T \)
$41$ \( T \)
$43$ \( -8 + T \)
$47$ \( T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( -14 + T \)
$67$ \( -16 + T \)
$71$ \( T \)
$73$ \( -10 + T \)
$79$ \( 4 + T \)
$83$ \( T \)
$89$ \( T \)
$97$ \( 14 + T \)
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