Newform orbit 2034.3.d.a

• Label: 2034.3.d.a
• Level: $2034$
• Weight: $3$
• Character orbit: 2034.d
• Analytic conductor: $55.422$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2034 = 2 \cdot 3^{2} \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2034.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(55.4224857709\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 72 q^{4} - 8 q^{7} + 144 q^{16} + 36 q^{25} + 16 q^{28} + 64 q^{31} + 108 q^{49} - 80 q^{61} - 288 q^{64} + 248 q^{82} - 164 q^{85} + 516 q^{91} - 420 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2033.1		−	1.41421i		0		−2.00000			4.88752				0		−5.78081					2.82843i		0			−	6.91200i
2033.2			1.41421i		0		−2.00000			4.88752				0		−5.78081				−	2.82843i		0				6.91200i
2033.3		−	1.41421i		0		−2.00000			8.53661				0		−3.58070					2.82843i		0			−	12.0726i
2033.4			1.41421i		0		−2.00000			8.53661				0		−3.58070				−	2.82843i		0				12.0726i
2033.5		−	1.41421i		0		−2.00000			2.30035				0		−13.1969					2.82843i		0			−	3.25319i
2033.6			1.41421i		0		−2.00000			2.30035				0		−13.1969				−	2.82843i		0				3.25319i
2033.7		−	1.41421i		0		−2.00000			−2.80308				0		4.63324					2.82843i		0				3.96415i
2033.8			1.41421i		0		−2.00000			−2.80308				0		4.63324				−	2.82843i		0			−	3.96415i
2033.9		−	1.41421i		0		−2.00000			2.80308				0		4.63324					2.82843i		0			−	3.96415i
2033.10			1.41421i		0		−2.00000			2.80308				0		4.63324				−	2.82843i		0				3.96415i
2033.11		−	1.41421i		0		−2.00000			−8.53661				0		−3.58070					2.82843i		0				12.0726i
2033.12			1.41421i		0		−2.00000			−8.53661				0		−3.58070				−	2.82843i		0			−	12.0726i
2033.13		−	1.41421i		0		−2.00000			3.08580				0		9.93072					2.82843i		0			−	4.36398i
2033.14			1.41421i		0		−2.00000			3.08580				0		9.93072				−	2.82843i		0				4.36398i
2033.15		−	1.41421i		0		−2.00000			−4.78233				0		−4.28693					2.82843i		0				6.76323i
2033.16			1.41421i		0		−2.00000			−4.78233				0		−4.28693				−	2.82843i		0			−	6.76323i
2033.17		−	1.41421i		0		−2.00000			1.48971				0		9.64045					2.82843i		0			−	2.10677i
2033.18			1.41421i		0		−2.00000			1.48971				0		9.64045				−	2.82843i		0				2.10677i
2033.19		−	1.41421i		0		−2.00000			4.78233				0		−4.28693					2.82843i		0			−	6.76323i
2033.20			1.41421i		0		−2.00000			4.78233				0		−4.28693				−	2.82843i		0				6.76323i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
113.b	even	2	1	inner
339.c	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2034.3.d.a	✓	36
3.b	odd	2	1	inner	2034.3.d.a	✓	36
113.b	even	2	1	inner	2034.3.d.a	✓	36
339.c	odd	2	1	inner	2034.3.d.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2034.3.d.a	✓	36	1.a	even	1	1	trivial
2034.3.d.a	✓	36	3.b	odd	2	1	inner
2034.3.d.a	✓	36	113.b	even	2	1	inner
2034.3.d.a	✓	36	339.c	odd	2	1	inner