Newform orbit 1512.2.t.d

• Label: 1512.2.t.d
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.t
• Analytic conductor: $12.073$
• Analytic rank: $0$
• Dimension: $22$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.0733807856\)
Analytic rank:	\(0\)
Dimension:	\(22\)
Relative dimension:	\(11\) over \(\Q(\zeta_{3})\)
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
289.1		0			0			0		−3.84095				0		0.676469	+	2.55781i		0			0			0
289.2		0			0			0		−2.66802				0		1.94471	−	1.79391i		0			0			0
289.3		0			0			0		−1.85591				0		−2.60465	+	0.464545i		0			0			0
289.4		0			0			0		−1.68316				0		0.960133	−	2.46539i		0			0			0
289.5		0			0			0		−0.340200				0		1.09748	+	2.40739i		0			0			0
289.6		0			0			0		0.481387				0		2.53326	+	0.763277i		0			0			0
289.7		0			0			0		1.58188				0		−1.80922	−	1.93047i		0			0			0
289.8		0			0			0		1.83657				0		2.45061	−	0.997255i		0			0			0
289.9		0			0			0		2.52290				0		−1.07705	−	2.41660i		0			0			0
289.10		0			0			0		3.43592				0		−1.83889	+	1.90223i		0			0			0
289.11		0			0			0		3.52959				0		1.16715	+	2.37440i		0			0			0
361.1		0			0			0		−3.84095				0		0.676469	−	2.55781i		0			0			0
361.2		0			0			0		−2.66802				0		1.94471	+	1.79391i		0			0			0
361.3		0			0			0		−1.85591				0		−2.60465	−	0.464545i		0			0			0
361.4		0			0			0		−1.68316				0		0.960133	+	2.46539i		0			0			0
361.5		0			0			0		−0.340200				0		1.09748	−	2.40739i		0			0			0
361.6		0			0			0		0.481387				0		2.53326	−	0.763277i		0			0			0
361.7		0			0			0		1.58188				0		−1.80922	+	1.93047i		0			0			0
361.8		0			0			0		1.83657				0		2.45061	+	0.997255i		0			0			0
361.9		0			0			0		2.52290				0		−1.07705	+	2.41660i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.g	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1512.2.t.d		22
3.b	odd	2	1		504.2.t.d	yes	22
4.b	odd	2	1		3024.2.t.l		22
7.c	even	3	1		1512.2.q.c		22
9.c	even	3	1		1512.2.q.c		22
9.d	odd	6	1		504.2.q.d	✓	22
12.b	even	2	1		1008.2.t.k		22
21.h	odd	6	1		504.2.q.d	✓	22
28.g	odd	6	1		3024.2.q.k		22
36.f	odd	6	1		3024.2.q.k		22
36.h	even	6	1		1008.2.q.k		22
63.g	even	3	1	inner	1512.2.t.d		22
63.n	odd	6	1		504.2.t.d	yes	22
84.n	even	6	1		1008.2.q.k		22
252.o	even	6	1		1008.2.t.k		22
252.bl	odd	6	1		3024.2.t.l		22

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.2.q.d	✓	22	9.d	odd	6	1
504.2.q.d	✓	22	21.h	odd	6	1
504.2.t.d	yes	22	3.b	odd	2	1
504.2.t.d	yes	22	63.n	odd	6	1
1008.2.q.k		22	36.h	even	6	1
1008.2.q.k		22	84.n	even	6	1
1008.2.t.k		22	12.b	even	2	1
1008.2.t.k		22	252.o	even	6	1
1512.2.q.c		22	7.c	even	3	1
1512.2.q.c		22	9.c	even	3	1
1512.2.t.d		22	1.a	even	1	1	trivial
1512.2.t.d		22	63.g	even	3	1	inner
3024.2.q.k		22	28.g	odd	6	1
3024.2.q.k		22	36.f	odd	6	1
3024.2.t.l		22	4.b	odd	2	1
3024.2.t.l		22	252.bl	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^11 - 3*T5^10 - 28*T5^9 + 85*T5^8 + 249*T5^7 - 766*T5^6 - 841*T5^5 + 2700*T5^4 + 880*T5^3 - 3400*T5^2 + 225*T5 + 466