Newform orbit 760.2.bx.a

• Label: 760.2.bx.a
• Level: $760$
• Weight: $2$
• Character orbit: 760.bx
• Analytic conductor: $6.069$
• Analytic rank: $0$
• Dimension: $24$
• CM discriminant: -40
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.bx (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.06863055362\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(4\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 48 q^{14} + 48 q^{26} + 60 q^{35} - 12 q^{41} + 24 q^{44} - 84 q^{49} + 96 q^{64} - 180 q^{65} - 96 q^{74} + 72 q^{76} + 168 q^{89} + 96 q^{91} + 36 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
59.1	−1.39273	−	0.245576i		0		1.87939	+	0.684040i	−2.10122	+	0.764780i		0		−1.61753	−	2.80164i	−2.44949	−	1.41421i	−0.520945	−	2.95442i	3.11424	−	0.549124i
59.2	−1.39273	−	0.245576i		0		1.87939	+	0.684040i	2.10122	−	0.764780i		0		2.58491	+	4.47719i	−2.44949	−	1.41421i	−0.520945	−	2.95442i	−3.11424	+	0.549124i
59.3	1.39273	+	0.245576i		0		1.87939	+	0.684040i	−2.10122	+	0.764780i		0		−2.58491	−	4.47719i	2.44949	+	1.41421i	−0.520945	−	2.95442i	−3.11424	+	0.549124i
59.4	1.39273	+	0.245576i		0		1.87939	+	0.684040i	2.10122	−	0.764780i		0		1.61753	+	2.80164i	2.44949	+	1.41421i	−0.520945	−	2.95442i	3.11424	−	0.549124i
219.1	−1.39273	+	0.245576i		0		1.87939	−	0.684040i	−2.10122	−	0.764780i		0		−1.61753	+	2.80164i	−2.44949	+	1.41421i	−0.520945	+	2.95442i	3.11424	+	0.549124i
219.2	−1.39273	+	0.245576i		0		1.87939	−	0.684040i	2.10122	+	0.764780i		0		2.58491	−	4.47719i	−2.44949	+	1.41421i	−0.520945	+	2.95442i	−3.11424	−	0.549124i
219.3	1.39273	−	0.245576i		0		1.87939	−	0.684040i	−2.10122	−	0.764780i		0		−2.58491	+	4.47719i	2.44949	−	1.41421i	−0.520945	+	2.95442i	−3.11424	−	0.549124i
219.4	1.39273	−	0.245576i		0		1.87939	−	0.684040i	2.10122	+	0.764780i		0		1.61753	−	2.80164i	2.44949	−	1.41421i	−0.520945	+	2.95442i	3.11424	+	0.549124i
299.1	−0.483690	−	1.32893i		0		−1.53209	+	1.28558i	−1.71293	−	1.43732i		0		−2.62197	−	4.54138i	2.44949	+	1.41421i	2.81908	+	1.02606i	−1.08156	+	2.97157i
299.2	−0.483690	−	1.32893i		0		−1.53209	+	1.28558i	1.71293	+	1.43732i		0		0.803888	+	1.39238i	2.44949	+	1.41421i	2.81908	+	1.02606i	1.08156	−	2.97157i
299.3	0.483690	+	1.32893i		0		−1.53209	+	1.28558i	−1.71293	−	1.43732i		0		−0.803888	−	1.39238i	−2.44949	−	1.41421i	2.81908	+	1.02606i	1.08156	−	2.97157i
299.4	0.483690	+	1.32893i		0		−1.53209	+	1.28558i	1.71293	+	1.43732i		0		2.62197	+	4.54138i	−2.44949	−	1.41421i	2.81908	+	1.02606i	−1.08156	+	2.97157i
459.1	−0.909039	+	1.08335i		0		−0.347296	−	1.96962i	−0.388289	+	2.20210i		0		1.00444	+	1.73974i	2.44949	+	1.41421i	−2.29813	+	1.92836i	−2.03267	−	2.42245i
459.2	−0.909039	+	1.08335i		0		−0.347296	−	1.96962i	0.388289	−	2.20210i		0		1.78102	+	3.08481i	2.44949	+	1.41421i	−2.29813	+	1.92836i	2.03267	+	2.42245i
459.3	0.909039	−	1.08335i		0		−0.347296	−	1.96962i	−0.388289	+	2.20210i		0		−1.78102	−	3.08481i	−2.44949	−	1.41421i	−2.29813	+	1.92836i	2.03267	+	2.42245i
459.4	0.909039	−	1.08335i		0		−0.347296	−	1.96962i	0.388289	−	2.20210i		0		−1.00444	−	1.73974i	−2.44949	−	1.41421i	−2.29813	+	1.92836i	−2.03267	−	2.42245i
659.1	−0.909039	−	1.08335i		0		−0.347296	+	1.96962i	−0.388289	−	2.20210i		0		1.00444	−	1.73974i	2.44949	−	1.41421i	−2.29813	−	1.92836i	−2.03267	+	2.42245i
659.2	−0.909039	−	1.08335i		0		−0.347296	+	1.96962i	0.388289	+	2.20210i		0		1.78102	−	3.08481i	2.44949	−	1.41421i	−2.29813	−	1.92836i	2.03267	−	2.42245i
659.3	0.909039	+	1.08335i		0		−0.347296	+	1.96962i	−0.388289	−	2.20210i		0		−1.78102	+	3.08481i	−2.44949	+	1.41421i	−2.29813	−	1.92836i	2.03267	−	2.42245i
659.4	0.909039	+	1.08335i		0		−0.347296	+	1.96962i	0.388289	+	2.20210i		0		−1.00444	+	1.73974i	−2.44949	+	1.41421i	−2.29813	−	1.92836i	−2.03267	+	2.42245i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
40.e	odd	2	1	CM by \(\Q(\sqrt{-10}) \)
5.b	even	2	1	inner
8.d	odd	2	1	inner
19.f	odd	18	1	inner
95.o	odd	18	1	inner
152.v	even	18	1	inner
760.bx	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	760.2.bx.a	✓	24
5.b	even	2	1	inner	760.2.bx.a	✓	24
8.d	odd	2	1	inner	760.2.bx.a	✓	24
19.f	odd	18	1	inner	760.2.bx.a	✓	24
40.e	odd	2	1	CM	760.2.bx.a	✓	24
95.o	odd	18	1	inner	760.2.bx.a	✓	24
152.v	even	18	1	inner	760.2.bx.a	✓	24
760.bx	even	18	1	inner	760.2.bx.a	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
760.2.bx.a	✓	24	1.a	even	1	1	trivial
760.2.bx.a	✓	24	5.b	even	2	1	inner
760.2.bx.a	✓	24	8.d	odd	2	1	inner
760.2.bx.a	✓	24	19.f	odd	18	1	inner
760.2.bx.a	✓	24	40.e	odd	2	1	CM
760.2.bx.a	✓	24	95.o	odd	18	1	inner
760.2.bx.a	✓	24	152.v	even	18	1	inner
760.2.bx.a	✓	24	760.bx	even	18	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{2}^{\mathrm{new}}(760, [\chi])\).