Newform orbit 2592.2.i.u

• Label: 2592.2.i.u
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.i
• Analytic conductor: $20.697$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.6972242039\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 864)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-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.

\(f(q)\)	\(=\)	\( q + 2 \zeta_{6} q^{5} + ( - \zeta_{6} + 1) q^{7}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} + q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\)	\(325\)	\(1217\)	\(2431\)
\(\chi(n)\)	\(1\)	\(-\zeta_{6}\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

865.1

0.500000	+	0.866025i
0.500000	−	0.866025i

0

0

0

1.00000

+

1.73205i

0

0.500000

−

0.866025i

0

0

0

1729.1

0

0

0

1.00000

−

1.73205i

0

0.500000

+

0.866025i

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2592.2.i.u		2
3.b	odd	2	1		2592.2.i.f		2
4.b	odd	2	1		2592.2.i.s		2
9.c	even	3	1		864.2.a.b	✓	1
9.c	even	3	1	inner	2592.2.i.u		2
9.d	odd	6	1		864.2.a.j	yes	1
9.d	odd	6	1		2592.2.i.f		2
12.b	even	2	1		2592.2.i.d		2
36.f	odd	6	1		864.2.a.c	yes	1
36.f	odd	6	1		2592.2.i.s		2
36.h	even	6	1		864.2.a.k	yes	1
36.h	even	6	1		2592.2.i.d		2
72.j	odd	6	1		1728.2.a.f		1
72.l	even	6	1		1728.2.a.g		1
72.n	even	6	1		1728.2.a.v		1
72.p	odd	6	1		1728.2.a.w		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
864.2.a.b	✓	1	9.c	even	3	1
864.2.a.c	yes	1	36.f	odd	6	1
864.2.a.j	yes	1	9.d	odd	6	1
864.2.a.k	yes	1	36.h	even	6	1
1728.2.a.f		1	72.j	odd	6	1
1728.2.a.g		1	72.l	even	6	1
1728.2.a.v		1	72.n	even	6	1
1728.2.a.w		1	72.p	odd	6	1
2592.2.i.d		2	12.b	even	2	1
2592.2.i.d		2	36.h	even	6	1
2592.2.i.f		2	3.b	odd	2	1
2592.2.i.f		2	9.d	odd	6	1
2592.2.i.s		2	4.b	odd	2	1
2592.2.i.s		2	36.f	odd	6	1
2592.2.i.u		2	1.a	even	1	1	trivial
2592.2.i.u		2	9.c	even	3	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2592, [\chi])\):

\( T_{5}^{2} - 2T_{5} + 4 \)

\( T_{7}^{2} - T_{7} + 1 \)

\( T_{11}^{2} + 2T_{11} + 4 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 2T + 4 \)
$7$	\( T^{2} - T + 1 \)
$11$	\( T^{2} + 2T + 4 \)