Newform orbit 2304.4.c.n

• Label: 2304.4.c.n
• Level: $2304$
• Weight: $4$
• Character orbit: 2304.c
• Analytic conductor: $135.940$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2304.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(135.940400653\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 72)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2303.1		0			0			0			−	19.8898i		0				12.9042i		0			0			0
2303.2		0			0			0				19.8898i		0			−	12.9042i		0			0			0
2303.3		0			0			0			−	4.33351i		0			−	28.4234i		0			0			0
2303.4		0			0			0				4.33351i		0				28.4234i		0			0			0
2303.5		0			0			0			−	19.8898i		0			−	12.9042i		0			0			0
2303.6		0			0			0				19.8898i		0				12.9042i		0			0			0
2303.7		0			0			0			−	5.96794i		0				4.64674i		0			0			0
2303.8		0			0			0				5.96794i		0			−	4.64674i		0			0			0
2303.9		0			0			0			−	19.8898i		0				12.9042i		0			0			0
2303.10		0			0			0				19.8898i		0			−	12.9042i		0			0			0
2303.11		0			0			0			−	5.96794i		0			−	4.64674i		0			0			0
2303.12		0			0			0				5.96794i		0				4.64674i		0			0			0
2303.13		0			0			0			−	4.33351i		0				28.4234i		0			0			0
2303.14		0			0			0				4.33351i		0			−	28.4234i		0			0			0
2303.15		0			0			0			−	4.33351i		0				28.4234i		0			0			0
2303.16		0			0			0				4.33351i		0			−	28.4234i		0			0			0
2303.17		0			0			0			−	4.33351i		0			−	28.4234i		0			0			0
2303.18		0			0			0				4.33351i		0				28.4234i		0			0			0
2303.19		0			0			0			−	19.8898i		0			−	12.9042i		0			0			0
2303.20		0			0			0				19.8898i		0				12.9042i		0			0			0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2304.4.c.n		24
3.b	odd	2	1	inner	2304.4.c.n		24
4.b	odd	2	1	inner	2304.4.c.n		24
8.b	even	2	1	inner	2304.4.c.n		24
8.d	odd	2	1	inner	2304.4.c.n		24
12.b	even	2	1	inner	2304.4.c.n		24
16.e	even	4	1		72.4.f.a	✓	12
16.e	even	4	1		288.4.f.a		12
16.f	odd	4	1		72.4.f.a	✓	12
16.f	odd	4	1		288.4.f.a		12
24.f	even	2	1	inner	2304.4.c.n		24
24.h	odd	2	1	inner	2304.4.c.n		24
48.i	odd	4	1		72.4.f.a	✓	12
48.i	odd	4	1		288.4.f.a		12
48.k	even	4	1		72.4.f.a	✓	12
48.k	even	4	1		288.4.f.a		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
72.4.f.a	✓	12	16.e	even	4	1
72.4.f.a	✓	12	16.f	odd	4	1
72.4.f.a	✓	12	48.i	odd	4	1
72.4.f.a	✓	12	48.k	even	4	1
288.4.f.a		12	16.e	even	4	1
288.4.f.a		12	16.f	odd	4	1
288.4.f.a		12	48.i	odd	4	1
288.4.f.a		12	48.k	even	4	1
2304.4.c.n		24	1.a	even	1	1	trivial
2304.4.c.n		24	3.b	odd	2	1	inner
2304.4.c.n		24	4.b	odd	2	1	inner
2304.4.c.n		24	8.b	even	2	1	inner
2304.4.c.n		24	8.d	odd	2	1	inner
2304.4.c.n		24	12.b	even	2	1	inner
2304.4.c.n		24	24.f	even	2	1	inner
2304.4.c.n		24	24.h	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(2304, [\chi])\):

\( T_{5}^{6} + 450T_{5}^{4} + 22188T_{5}^{2} + 264600 \)

\( T_{11}^{6} - 4440T_{11}^{4} + 4605120T_{11}^{2} - 15323648 \)

\( T_{13}^{6} - 5700T_{13}^{4} + 7291056T_{13}^{2} - 2534148288 \)