Newform orbit 2400.3.p.c

• Label: 2400.3.p.c
• Level: $2400$
• Weight: $3$
• Character orbit: 2400.p
• Analytic conductor: $65.395$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2400.p (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(65.3952634465\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	no (minimal twist has level 600)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 96 q^{9} + 64 q^{11} - 64 q^{19} + 256 q^{49} - 192 q^{51} + 256 q^{59} + 288 q^{81} + 960 q^{91} - 192 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1999.1		0			−	1.73205i		0			0			0		10.9881				0		−3.00000				0
1999.2		0				1.73205i		0			0			0		10.9881				0		−3.00000				0
1999.3		0			−	1.73205i		0			0			0		−2.13685				0		−3.00000				0
1999.4		0				1.73205i		0			0			0		−2.13685				0		−3.00000				0
1999.5		0			−	1.73205i		0			0			0		11.8458				0		−3.00000				0
1999.6		0				1.73205i		0			0			0		11.8458				0		−3.00000				0
1999.7		0			−	1.73205i		0			0			0		−0.610378				0		−3.00000				0
1999.8		0				1.73205i		0			0			0		−0.610378				0		−3.00000				0
1999.9		0			−	1.73205i		0			0			0		−2.71814				0		−3.00000				0
1999.10		0				1.73205i		0			0			0		−2.71814				0		−3.00000				0
1999.11		0			−	1.73205i		0			0			0		6.06690				0		−3.00000				0
1999.12		0				1.73205i		0			0			0		6.06690				0		−3.00000				0
1999.13		0			−	1.73205i		0			0			0		0.610378				0		−3.00000				0
1999.14		0				1.73205i		0			0			0		0.610378				0		−3.00000				0
1999.15		0			−	1.73205i		0			0			0		8.37149				0		−3.00000				0
1999.16		0				1.73205i		0			0			0		8.37149				0		−3.00000				0
1999.17		0			−	1.73205i		0			0			0		2.13685				0		−3.00000				0
1999.18		0				1.73205i		0			0			0		2.13685				0		−3.00000				0
1999.19		0			−	1.73205i		0			0			0		−6.06690				0		−3.00000				0
1999.20		0				1.73205i		0			0			0		−6.06690				0		−3.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
8.d	odd	2	1	inner
40.e	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2400.3.p.c		32
4.b	odd	2	1		600.3.p.c		32
5.b	even	2	1	inner	2400.3.p.c		32
5.c	odd	4	1		2400.3.g.c		16
5.c	odd	4	1		2400.3.g.d		16
8.b	even	2	1		600.3.p.c		32
8.d	odd	2	1	inner	2400.3.p.c		32
20.d	odd	2	1		600.3.p.c		32
20.e	even	4	1		600.3.g.b	✓	16
20.e	even	4	1		600.3.g.c	yes	16
40.e	odd	2	1	inner	2400.3.p.c		32
40.f	even	2	1		600.3.p.c		32
40.i	odd	4	1		600.3.g.b	✓	16
40.i	odd	4	1		600.3.g.c	yes	16
40.k	even	4	1		2400.3.g.c		16
40.k	even	4	1		2400.3.g.d		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
600.3.g.b	✓	16	20.e	even	4	1
600.3.g.b	✓	16	40.i	odd	4	1
600.3.g.c	yes	16	20.e	even	4	1
600.3.g.c	yes	16	40.i	odd	4	1
600.3.p.c		32	4.b	odd	2	1
600.3.p.c		32	8.b	even	2	1
600.3.p.c		32	20.d	odd	2	1
600.3.p.c		32	40.f	even	2	1
2400.3.g.c		16	5.c	odd	4	1
2400.3.g.c		16	40.k	even	4	1
2400.3.g.d		16	5.c	odd	4	1
2400.3.g.d		16	40.k	even	4	1
2400.3.p.c		32	1.a	even	1	1	trivial
2400.3.p.c		32	5.b	even	2	1	inner
2400.3.p.c		32	8.d	odd	2	1	inner
2400.3.p.c		32	40.e	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^16 - 456*T7^14 + 80796*T7^12 - 7020664*T7^10 + 309600966*T7^8 - 6400008312*T7^6 + 49723657372*T7^4 - 129295497672*T7^2 + 41593807233