Newform orbit 2340.2.y.b

• Label: 2340.2.y.b
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.y
• Analytic conductor: $18.685$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.6849940730\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 24 * q + 4 * q^5 - 8 * q^7 + 8 * q^17 + 8 * q^23 + 16 * q^25 - 32 * q^29 - 8 * q^35 + 16 * q^37 - 8 * q^43 + 40 * q^47 + 8 * q^53 + 8 * q^55 - 56 * q^59 + 8 * q^61 + 4 * q^65 - 16 * q^67 + 72 * q^77 + 32 * q^83 - 32 * q^85 - 128 * q^89 - 8 * q^91 - 16 * q^95 + 8 * q^97

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1		0			0			0		−2.15870	+	0.583115i		0		−1.95569	+	1.95569i		0			0			0
53.2		0			0			0		−2.02935	−	0.939016i		0		−0.932729	+	0.932729i		0			0			0
53.3		0			0			0		−1.41774	−	1.72916i		0		1.36664	−	1.36664i		0			0			0
53.4		0			0			0		−1.23903	−	1.86140i		0		−0.157336	+	0.157336i		0			0			0
53.5		0			0			0		−1.12174	+	1.93434i		0		−2.61067	+	2.61067i		0			0			0
53.6		0			0			0		−0.686017	+	2.12823i		0		0.778541	−	0.778541i		0			0			0
53.7		0			0			0		1.17829	−	1.90043i		0		−0.865311	+	0.865311i		0			0			0
53.8		0			0			0		1.25978	+	1.84742i		0		−1.73394	+	1.73394i		0			0			0
53.9		0			0			0		1.80799	−	1.31574i		0		−0.602482	+	0.602482i		0			0			0
53.10		0			0			0		2.01597	−	0.967408i		0		3.08512	−	3.08512i		0			0			0
53.11		0			0			0		2.17472	+	0.520203i		0		−3.20978	+	3.20978i		0			0			0
53.12		0			0			0		2.21583	−	0.300151i		0		2.83763	−	2.83763i		0			0			0
1457.1		0			0			0		−2.15870	−	0.583115i		0		−1.95569	−	1.95569i		0			0			0
1457.2		0			0			0		−2.02935	+	0.939016i		0		−0.932729	−	0.932729i		0			0			0
1457.3		0			0			0		−1.41774	+	1.72916i		0		1.36664	+	1.36664i		0			0			0
1457.4		0			0			0		−1.23903	+	1.86140i		0		−0.157336	−	0.157336i		0			0			0
1457.5		0			0			0		−1.12174	−	1.93434i		0		−2.61067	−	2.61067i		0			0			0
1457.6		0			0			0		−0.686017	−	2.12823i		0		0.778541	+	0.778541i		0			0			0
1457.7		0			0			0		1.17829	+	1.90043i		0		−0.865311	−	0.865311i		0			0			0
1457.8		0			0			0		1.25978	−	1.84742i		0		−1.73394	−	1.73394i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
15.e	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2340.2.y.b	yes	24
3.b	odd	2	1		2340.2.y.a	✓	24
5.c	odd	4	1		2340.2.y.a	✓	24
15.e	even	4	1	inner	2340.2.y.b	yes	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2340.2.y.a	✓	24	3.b	odd	2	1
2340.2.y.a	✓	24	5.c	odd	4	1
2340.2.y.b	yes	24	1.a	even	1	1	trivial
2340.2.y.b	yes	24	15.e	even	4	1	inner