Newform orbit 3552.2.o.a

• Label: 3552.2.o.a
• Level: $3552$
• Weight: $2$
• Character orbit: 3552.o
• Analytic conductor: $28.363$
• Analytic rank: $0$
• Dimension: $76$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3552 = 2^{5} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3552.o (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(28.3628627980\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Twist minimal:	no (minimal twist has level 888)
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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q - 8 q^{7} - 76 q^{9} + 84 q^{25} - 8 q^{41} + 60 q^{49} + 8 q^{63} + 48 q^{65} + 16 q^{71} + 24 q^{73} + 76 q^{81}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2737.1		0			−	1.00000i		0		−4.06066				0		−3.70627				0		−1.00000				0
2737.2		0				1.00000i		0		−4.06066				0		−3.70627				0		−1.00000				0
2737.3		0			−	1.00000i		0		4.07371				0		2.80969				0		−1.00000				0
2737.4		0				1.00000i		0		4.07371				0		2.80969				0		−1.00000				0
2737.5		0			−	1.00000i		0		−1.36027				0		−1.05670				0		−1.00000				0
2737.6		0				1.00000i		0		−1.36027				0		−1.05670				0		−1.00000				0
2737.7		0			−	1.00000i		0		1.36027				0		−1.05670				0		−1.00000				0
2737.8		0				1.00000i		0		1.36027				0		−1.05670				0		−1.00000				0
2737.9		0			−	1.00000i		0		−3.45802				0		−2.64096				0		−1.00000				0
2737.10		0				1.00000i		0		−3.45802				0		−2.64096				0		−1.00000				0
2737.11		0			−	1.00000i		0		1.62896				0		0.552600				0		−1.00000				0
2737.12		0				1.00000i		0		1.62896				0		0.552600				0		−1.00000				0
2737.13		0			−	1.00000i		0		−1.62896				0		0.552600				0		−1.00000				0
2737.14		0				1.00000i		0		−1.62896				0		0.552600				0		−1.00000				0
2737.15		0			−	1.00000i		0		−0.598100				0		4.50845				0		−1.00000				0
2737.16		0				1.00000i		0		−0.598100				0		4.50845				0		−1.00000				0
2737.17		0			−	1.00000i		0		−2.00896				0		−1.76422				0		−1.00000				0
2737.18		0				1.00000i		0		−2.00896				0		−1.76422				0		−1.00000				0
2737.19		0			−	1.00000i		0		0.00220932				0		0.375319				0		−1.00000				0
2737.20		0				1.00000i		0		0.00220932				0		0.375319				0		−1.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.b	even	2	1	inner
37.b	even	2	1	inner
296.e	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3552.2.o.a		76
4.b	odd	2	1		888.2.o.a	✓	76
8.b	even	2	1	inner	3552.2.o.a		76
8.d	odd	2	1		888.2.o.a	✓	76
37.b	even	2	1	inner	3552.2.o.a		76
148.b	odd	2	1		888.2.o.a	✓	76
296.e	even	2	1	inner	3552.2.o.a		76
296.h	odd	2	1		888.2.o.a	✓	76

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
888.2.o.a	✓	76	4.b	odd	2	1
888.2.o.a	✓	76	8.d	odd	2	1
888.2.o.a	✓	76	148.b	odd	2	1
888.2.o.a	✓	76	296.h	odd	2	1
3552.2.o.a		76	1.a	even	1	1	trivial
3552.2.o.a		76	8.b	even	2	1	inner
3552.2.o.a		76	37.b	even	2	1	inner
3552.2.o.a		76	296.e	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(3552, [\chi])\).