Newform orbit 380.3.m.a

• Label: 380.3.m.a
• Level: $380$
• Weight: $3$
• Character orbit: 380.m
• Analytic conductor: $10.354$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.3542500457\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(18\) 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.

\(\operatorname{Tr}(f)(q) = \) 36 * q - 4 * q^3 + 10 * q^5 + 22 * q^7 - 24 * q^11 - 28 * q^13 - 16 * q^15 - 26 * q^17 + 104 * q^21 + 20 * q^23 - 18 * q^25 + 20 * q^27 - 56 * q^31 - 16 * q^33 - 110 * q^35 - 4 * q^37 + 120 * q^41 - 10 * q^43 - 168 * q^45 + 38 * q^47 - 24 * q^51 + 128 * q^53 + 136 * q^55 + 40 * q^61 + 34 * q^63 + 224 * q^65 + 220 * q^67 - 360 * q^71 - 66 * q^73 + 16 * q^75 - 62 * q^77 - 284 * q^81 + 556 * q^83 + 276 * q^85 - 72 * q^87 - 40 * q^91 - 200 * q^93 - 38 * q^95 - 376 * 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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
77.1		0		−4.00433	+	4.00433i		0		2.77525	−	4.15908i		0		5.61303	+	5.61303i		0			−	23.0694i		0
77.2		0		−3.78958	+	3.78958i		0		4.49689	+	2.18586i		0		−5.54614	−	5.54614i		0			−	19.7218i		0
77.3		0		−3.16890	+	3.16890i		0		−4.72076	−	1.64754i		0		−2.39561	−	2.39561i		0			−	11.0839i		0
77.4		0		−2.45591	+	2.45591i		0		1.27755	+	4.83403i		0		6.94958	+	6.94958i		0			−	3.06300i		0
77.5		0		−2.42478	+	2.42478i		0		1.05897	−	4.88657i		0		−7.91713	−	7.91713i		0			−	2.75914i		0
77.6		0		−2.28945	+	2.28945i		0		−3.24268	+	3.80592i		0		−1.61583	−	1.61583i		0			−	1.48314i		0
77.7		0		−1.90429	+	1.90429i		0		−3.85464	−	3.18461i		0		6.36530	+	6.36530i		0				1.74733i		0
77.8		0		−0.654756	+	0.654756i		0		3.69864	+	3.36453i		0		−5.77298	−	5.77298i		0				8.14259i		0
77.9		0		−0.650727	+	0.650727i		0		4.72692	−	1.62980i		0		4.72697	+	4.72697i		0				8.15311i		0
77.10		0		−0.260437	+	0.260437i		0		1.11582	−	4.87391i		0		−1.11767	−	1.11767i		0				8.86434i		0
77.11		0		1.21053	−	1.21053i		0		−4.93854	−	0.781541i		0		2.84579	+	2.84579i		0				6.06924i		0
77.12		0		1.41012	−	1.41012i		0		−2.59675	−	4.27281i		0		−3.41557	−	3.41557i		0				5.02314i		0
77.13		0		1.66875	−	1.66875i		0		4.68164	+	1.75564i		0		1.92669	+	1.92669i		0				3.43056i		0
77.14		0		1.69936	−	1.69936i		0		−1.79290	+	4.66750i		0		7.30539	+	7.30539i		0				3.22437i		0
77.15		0		3.08066	−	3.08066i		0		2.22917	+	4.47558i		0		1.64282	+	1.64282i		0			−	9.98098i		0
77.16		0		3.18663	−	3.18663i		0		4.23624	−	2.65599i		0		−6.53286	−	6.53286i		0			−	11.3092i		0
77.17		0		3.44783	−	3.44783i		0		0.848706	−	4.92744i		0		9.50258	+	9.50258i		0			−	14.7751i		0
77.18		0		3.89930	−	3.89930i		0		−4.99951	−	0.0697581i		0		−1.56436	−	1.56436i		0			−	21.4091i		0
153.1		0		−4.00433	−	4.00433i		0		2.77525	+	4.15908i		0		5.61303	−	5.61303i		0				23.0694i		0
153.2		0		−3.78958	−	3.78958i		0		4.49689	−	2.18586i		0		−5.54614	+	5.54614i		0				19.7218i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	380.3.m.a	✓	36
5.c	odd	4	1	inner	380.3.m.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
380.3.m.a	✓	36	1.a	even	1	1	trivial
380.3.m.a	✓	36	5.c	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(380, [\chi])\).