Newform orbit 2912.2.c.b

• Label: 2912.2.c.b
• Level: $2912$
• Weight: $2$
• Character orbit: 2912.c
• Analytic conductor: $23.252$
• Analytic rank: $0$
• Dimension: $38$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2912.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.2524370686\)
Analytic rank:	\(0\)
Dimension:	\(38\)
Twist minimal:	no (minimal twist has level 728)
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.

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 38 q^{7} - 46 q^{9} + 8 q^{15} + 20 q^{17} - 12 q^{23} - 50 q^{25} - 16 q^{31} - 8 q^{33} - 8 q^{39} + 8 q^{41} + 38 q^{49} + 8 q^{57} + 46 q^{63} + 20 q^{65} + 12 q^{79} + 62 q^{81} + 56 q^{87}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1457.1		0			−	3.25810i		0			−	1.19614i		0		−1.00000				0		−7.61524				0
1457.2		0			−	3.17321i		0				3.62722i		0		−1.00000				0		−7.06928				0
1457.3		0			−	3.05148i		0			−	3.70659i		0		−1.00000				0		−6.31151				0
1457.4		0			−	2.99675i		0				2.10333i		0		−1.00000				0		−5.98049				0
1457.5		0			−	2.79941i		0				3.17859i		0		−1.00000				0		−4.83671				0
1457.6		0			−	2.40918i		0			−	0.687773i		0		−1.00000				0		−2.80413				0
1457.7		0			−	2.33171i		0			−	0.889625i		0		−1.00000				0		−2.43685				0
1457.8		0			−	2.23317i		0			−	1.70457i		0		−1.00000				0		−1.98704				0
1457.9		0			−	2.10063i		0			−	0.418613i		0		−1.00000				0		−1.41263				0
1457.10		0			−	1.89594i		0				1.04788i		0		−1.00000				0		−0.594602				0
1457.11		0			−	1.67830i		0				0.0254406i		0		−1.00000				0		0.183319				0
1457.12		0			−	1.48422i		0			−	4.04476i		0		−1.00000				0		0.797083				0
1457.13		0			−	1.13807i		0				2.82904i		0		−1.00000				0		1.70480				0
1457.14		0			−	1.07539i		0			−	3.29373i		0		−1.00000				0		1.84353				0
1457.15		0			−	0.912057i		0				2.01280i		0		−1.00000				0		2.16815				0
1457.16		0			−	0.560000i		0				0.293198i		0		−1.00000				0		2.68640				0
1457.17		0			−	0.472093i		0				4.35100i		0		−1.00000				0		2.77713				0
1457.18		0			−	0.273626i		0				2.12501i		0		−1.00000				0		2.92513				0
1457.19		0			−	0.192506i		0				2.98429i		0		−1.00000				0		2.96294				0
1457.20		0				0.192506i		0			−	2.98429i		0		−1.00000				0		2.96294				0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2912.2.c.b		38
4.b	odd	2	1		728.2.c.b	✓	38
8.b	even	2	1	inner	2912.2.c.b		38
8.d	odd	2	1		728.2.c.b	✓	38

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
728.2.c.b	✓	38	4.b	odd	2	1
728.2.c.b	✓	38	8.d	odd	2	1
2912.2.c.b		38	1.a	even	1	1	trivial
2912.2.c.b		38	8.b	even	2	1	inner