Newform orbit 2912.2.h.a

• Label: 2912.2.h.a
• Level: $2912$
• Weight: $2$
• Character orbit: 2912.h
• Analytic conductor: $23.252$
• Analytic rank: $0$
• Dimension: $48$
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(23.2524370686\)
Analytic rank:	\(0\)
Dimension:	\(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{9} + 4 q^{11} - 48 q^{13} + 48 q^{25} - 12 q^{35} + 4 q^{43} + 24 q^{45} + 40 q^{51} - 20 q^{63} + 4 q^{67} - 20 q^{77} + 64 q^{81} + 40 q^{87} - 20 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2575.1		0			−	3.37415i		0		−0.523773				0		2.30913	−	1.29148i		0		−8.38487				0
2575.2		0			−	3.10974i		0		3.50914				0		1.29016	−	2.30987i		0		−6.67047				0
2575.3		0			−	3.06517i		0		−4.00290				0		−1.79836	−	1.94059i		0		−6.39524				0
2575.4		0			−	3.03518i		0		−0.163903				0		−0.919188	+	2.48095i		0		−6.21234				0
2575.5		0			−	2.89173i		0		−2.33723				0		1.68858	+	2.03684i		0		−5.36210				0
2575.6		0			−	2.65471i		0		−0.263032				0		2.63919	+	0.186171i		0		−4.04746				0
2575.7		0			−	2.44281i		0		3.85137				0		−2.49284	+	0.886436i		0		−2.96733				0
2575.8		0			−	2.38356i		0		−1.68057				0		−1.10198	−	2.40533i		0		−2.68138				0
2575.9		0			−	2.32841i		0		2.37629				0		−2.43296	−	1.03956i		0		−2.42149				0
2575.10		0			−	2.21460i		0		1.27531				0		−0.643326	+	2.56635i		0		−1.90445				0
2575.11		0			−	1.92788i		0		−2.16680				0		−1.74001	+	1.99308i		0		−0.716713				0
2575.12		0			−	1.61368i		0		−3.74465				0		−0.220320	+	2.63656i		0		0.396033				0
2575.13		0			−	1.53313i		0		0.856056				0		−1.33356	−	2.28509i		0		0.649528				0
2575.14		0			−	1.48862i		0		1.02997				0		1.70779	−	2.02076i		0		0.784007				0
2575.15		0			−	1.40360i		0		−3.11493				0		2.64532	−	0.0479799i		0		1.02989				0
2575.16		0			−	1.35635i		0		2.01767				0		2.18534	+	1.49140i		0		1.16033				0
2575.17		0			−	1.31268i		0		2.82361				0		−0.786324	+	2.52620i		0		1.27686				0
2575.18		0			−	0.913695i		0		−3.26760				0		0.184260	−	2.63933i		0		2.16516				0
2575.19		0			−	0.788146i		0		−0.604005				0		2.57195	+	0.620533i		0		2.37883				0
2575.20		0			−	0.742757i		0		2.66467				0		−2.25806	−	1.37882i		0		2.44831				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
56.e	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.h.a		48
4.b	odd	2	1		728.2.h.a	✓	48
7.b	odd	2	1		2912.2.h.b		48
8.b	even	2	1		728.2.h.b	yes	48
8.d	odd	2	1		2912.2.h.b		48
28.d	even	2	1		728.2.h.b	yes	48
56.e	even	2	1	inner	2912.2.h.a		48
56.h	odd	2	1		728.2.h.a	✓	48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
728.2.h.a	✓	48	4.b	odd	2	1
728.2.h.a	✓	48	56.h	odd	2	1
728.2.h.b	yes	48	8.b	even	2	1
728.2.h.b	yes	48	28.d	even	2	1
2912.2.h.a		48	1.a	even	1	1	trivial
2912.2.h.a		48	56.e	even	2	1	inner
2912.2.h.b		48	7.b	odd	2	1
2912.2.h.b		48	8.d	odd	2	1