Newform orbit 1512.2.j.c

• Label: 1512.2.j.c
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.j
• Analytic conductor: $12.073$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.0733807856\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
323.1	−1.40936	−	0.117111i		0		1.97257	+	0.330101i	1.17792				0				1.00000i	−2.74140	−	0.696239i		0		−1.66010	−	0.137947i
323.2	−1.40936	+	0.117111i		0		1.97257	−	0.330101i	1.17792				0			−	1.00000i	−2.74140	+	0.696239i		0		−1.66010	+	0.137947i
323.3	−1.33436	−	0.468477i		0		1.56106	+	1.25024i	−3.47003				0				1.00000i	−1.49731	−	2.39959i		0		4.63028	+	1.62563i
323.4	−1.33436	+	0.468477i		0		1.56106	−	1.25024i	−3.47003				0			−	1.00000i	−1.49731	+	2.39959i		0		4.63028	−	1.62563i
323.5	−1.30241	−	0.551119i		0		1.39253	+	1.43556i	3.61017				0				1.00000i	−1.02248	−	2.63714i		0		−4.70192	−	1.98963i
323.6	−1.30241	+	0.551119i		0		1.39253	−	1.43556i	3.61017				0			−	1.00000i	−1.02248	+	2.63714i		0		−4.70192	+	1.98963i
323.7	−1.16953	−	0.795104i		0		0.735620	+	1.85980i	2.09311				0			−	1.00000i	0.618402	−	2.76000i		0		−2.44797	−	1.66424i
323.8	−1.16953	+	0.795104i		0		0.735620	−	1.85980i	2.09311				0				1.00000i	0.618402	+	2.76000i		0		−2.44797	+	1.66424i
323.9	−0.985454	−	1.01434i		0		−0.0577616	+	1.99917i	0.206991				0			−	1.00000i	2.08475	−	1.91150i		0		−0.203980	−	0.209959i
323.10	−0.985454	+	1.01434i		0		−0.0577616	−	1.99917i	0.206991				0				1.00000i	2.08475	+	1.91150i		0		−0.203980	+	0.209959i
323.11	−0.971008	−	1.02818i		0		−0.114288	+	1.99673i	−2.21305				0				1.00000i	2.16396	−	1.82133i		0		2.14889	+	2.27540i
323.12	−0.971008	+	1.02818i		0		−0.114288	−	1.99673i	−2.21305				0			−	1.00000i	2.16396	+	1.82133i		0		2.14889	−	2.27540i
323.13	−0.481042	−	1.32989i		0		−1.53720	+	1.27946i	−0.436221				0				1.00000i	2.44100	+	1.42882i		0		0.209841	+	0.580125i
323.14	−0.481042	+	1.32989i		0		−1.53720	−	1.27946i	−0.436221				0			−	1.00000i	2.44100	−	1.42882i		0		0.209841	−	0.580125i
323.15	−0.154052	−	1.40580i		0		−1.95254	+	0.433131i	−0.162025				0			−	1.00000i	0.909686	+	2.67815i		0		0.0249602	+	0.227774i
323.16	−0.154052	+	1.40580i		0		−1.95254	−	0.433131i	−0.162025				0				1.00000i	0.909686	−	2.67815i		0		0.0249602	−	0.227774i
323.17	0.154052	−	1.40580i		0		−1.95254	−	0.433131i	0.162025				0				1.00000i	−0.909686	+	2.67815i		0		0.0249602	−	0.227774i
323.18	0.154052	+	1.40580i		0		−1.95254	+	0.433131i	0.162025				0			−	1.00000i	−0.909686	−	2.67815i		0		0.0249602	+	0.227774i
323.19	0.481042	−	1.32989i		0		−1.53720	−	1.27946i	0.436221				0			−	1.00000i	−2.44100	+	1.42882i		0		0.209841	−	0.580125i
323.20	0.481042	+	1.32989i		0		−1.53720	+	1.27946i	0.436221				0				1.00000i	−2.44100	−	1.42882i		0		0.209841	+	0.580125i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.d	odd	2	1	inner
24.f	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1512.2.j.c	✓	32
3.b	odd	2	1	inner	1512.2.j.c	✓	32
4.b	odd	2	1		6048.2.j.c		32
8.b	even	2	1		6048.2.j.c		32
8.d	odd	2	1	inner	1512.2.j.c	✓	32
12.b	even	2	1		6048.2.j.c		32
24.f	even	2	1	inner	1512.2.j.c	✓	32
24.h	odd	2	1		6048.2.j.c		32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1512.2.j.c	✓	32	1.a	even	1	1	trivial
1512.2.j.c	✓	32	3.b	odd	2	1	inner
1512.2.j.c	✓	32	8.d	odd	2	1	inner
1512.2.j.c	✓	32	24.f	even	2	1	inner
6048.2.j.c		32	4.b	odd	2	1
6048.2.j.c		32	8.b	even	2	1
6048.2.j.c		32	12.b	even	2	1
6048.2.j.c		32	24.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{16} - 36T_{5}^{14} + 468T_{5}^{12} - 2684T_{5}^{10} + 6806T_{5}^{8} - 6300T_{5}^{6} + 1300T_{5}^{4} - 68T_{5}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(1512, [\chi])\).