Newform orbit 2100.2.s.c

• Label: 2100.2.s.c
• Level: $2100$
• Weight: $2$
• Character orbit: 2100.s
• Analytic conductor: $16.769$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(16.7685844245\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1457.1		0		−1.73156	−	0.0412661i		0			0			0		0.707107	+	0.707107i		0		2.99659	+	0.142909i		0
1457.2		0		−1.69214	+	0.369667i		0			0			0		0.707107	+	0.707107i		0		2.72669	−	1.25106i		0
1457.3		0		−1.63431	+	0.573626i		0			0			0		−0.707107	−	0.707107i		0		2.34191	−	1.87496i		0
1457.4		0		−1.28800	−	1.15804i		0			0			0		−0.707107	−	0.707107i		0		0.317883	+	2.98311i		0
1457.5		0		−1.15804	−	1.28800i		0			0			0		0.707107	+	0.707107i		0		−0.317883	+	2.98311i		0
1457.6		0		−0.573626	+	1.63431i		0			0			0		−0.707107	−	0.707107i		0		−2.34191	−	1.87496i		0
1457.7		0		−0.369667	+	1.69214i		0			0			0		0.707107	+	0.707107i		0		−2.72669	−	1.25106i		0
1457.8		0		−0.0412661	−	1.73156i		0			0			0		−0.707107	−	0.707107i		0		−2.99659	+	0.142909i		0
1457.9		0		0.0412661	+	1.73156i		0			0			0		0.707107	+	0.707107i		0		−2.99659	+	0.142909i		0
1457.10		0		0.369667	−	1.69214i		0			0			0		−0.707107	−	0.707107i		0		−2.72669	−	1.25106i		0
1457.11		0		0.573626	−	1.63431i		0			0			0		0.707107	+	0.707107i		0		−2.34191	−	1.87496i		0
1457.12		0		1.15804	+	1.28800i		0			0			0		−0.707107	−	0.707107i		0		−0.317883	+	2.98311i		0
1457.13		0		1.28800	+	1.15804i		0			0			0		0.707107	+	0.707107i		0		0.317883	+	2.98311i		0
1457.14		0		1.63431	−	0.573626i		0			0			0		0.707107	+	0.707107i		0		2.34191	−	1.87496i		0
1457.15		0		1.69214	−	0.369667i		0			0			0		−0.707107	−	0.707107i		0		2.72669	−	1.25106i		0
1457.16		0		1.73156	+	0.0412661i		0			0			0		−0.707107	−	0.707107i		0		2.99659	+	0.142909i		0
1793.1		0		−1.73156	+	0.0412661i		0			0			0		0.707107	−	0.707107i		0		2.99659	−	0.142909i		0
1793.2		0		−1.69214	−	0.369667i		0			0			0		0.707107	−	0.707107i		0		2.72669	+	1.25106i		0
1793.3		0		−1.63431	−	0.573626i		0			0			0		−0.707107	+	0.707107i		0		2.34191	+	1.87496i		0
1793.4		0		−1.28800	+	1.15804i		0			0			0		−0.707107	+	0.707107i		0		0.317883	−	2.98311i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.b	even	2	1	inner
5.c	odd	4	2	inner
15.d	odd	2	1	inner
15.e	even	4	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2100.2.s.c	✓	32
3.b	odd	2	1	inner	2100.2.s.c	✓	32
5.b	even	2	1	inner	2100.2.s.c	✓	32
5.c	odd	4	2	inner	2100.2.s.c	✓	32
15.d	odd	2	1	inner	2100.2.s.c	✓	32
15.e	even	4	2	inner	2100.2.s.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2100.2.s.c	✓	32	1.a	even	1	1	trivial
2100.2.s.c	✓	32	3.b	odd	2	1	inner
2100.2.s.c	✓	32	5.b	even	2	1	inner
2100.2.s.c	✓	32	5.c	odd	4	2	inner
2100.2.s.c	✓	32	15.d	odd	2	1	inner
2100.2.s.c	✓	32	15.e	even	4	2	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{11}^{8} + 60T_{11}^{6} + 962T_{11}^{4} + 4452T_{11}^{2} + 6253 \) acting on \(S_{2}^{\mathrm{new}}(2100, [\chi])\).