Newform orbit 387.4.t.a

• Label: 387.4.t.a
• Level: $387$
• Weight: $4$
• Character orbit: 387.t
• Analytic conductor: $22.834$
• Analytic rank: $0$
• Dimension: $88$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	387.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.8337391722\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(44\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88 q + 352 q^{4} + 36 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
80.1	−5.35626				0		20.6895			−9.40568	+	16.2911i		0		−2.42947	+	1.40265i	−67.9681				0		50.3792	−	87.2594i
80.2	−5.30328				0		20.1247			7.07670	−	12.2572i		0		−12.6733	+	7.31694i	−64.3008				0		−37.5297	+	65.0034i
80.3	−5.08922				0		17.9002			3.55145	−	6.15129i		0		4.36247	−	2.51867i	−50.3841				0		−18.0741	+	31.3053i
80.4	−4.98565				0		16.8567			−2.40518	+	4.16590i		0		25.3070	−	14.6110i	−44.1561				0		11.9914	−	20.7697i
80.5	−4.80928				0		15.1292			−7.70326	+	13.3424i		0		−7.35267	+	4.24507i	−34.2861				0		37.0471	−	64.1675i
80.6	−4.68138				0		13.9153			1.86944	−	3.23797i		0		19.0350	−	10.9898i	−27.6918				0		−8.75157	+	15.1582i
80.7	−4.47280				0		12.0060			5.25937	−	9.10950i		0		−24.0212	+	13.8686i	−17.9179				0		−23.5241	+	40.7450i
80.8	−3.59753				0		4.94224			5.46009	−	9.45715i		0		−4.91389	+	2.83704i	11.0004				0		−19.6428	+	34.0224i
80.9	−3.54391				0		4.55933			2.54970	−	4.41620i		0		2.47744	−	1.43035i	12.1935				0		−9.03590	+	15.6506i
80.10	−3.51282				0		4.33990			−6.78983	+	11.7603i		0		−27.6704	+	15.9755i	12.8573				0		23.8515	−	41.3119i
80.11	−3.41112				0		3.63575			−5.36870	+	9.29886i		0		−12.9550	+	7.47960i	14.8870				0		18.3133	−	31.7196i
80.12	−3.19991				0		2.23942			5.99131	−	10.3773i		0		21.5417	−	12.4371i	18.4333				0		−19.1716	+	33.2063i
80.13	−2.86531				0		0.209982			−6.86781	+	11.8954i		0		26.1422	−	15.0932i	22.3208				0		19.6784	−	34.0839i
80.14	−2.55364				0		−1.47894			−4.53563	+	7.85595i		0		−10.5674	+	6.10110i	24.2058				0		11.5824	−	20.0612i
80.15	−2.37418				0		−2.36326			−0.0767572	+	0.132947i		0		12.9661	−	7.48600i	24.6043				0		0.182235	−	0.315641i
80.16	−2.08595				0		−3.64883			10.2883	−	17.8199i		0		3.65093	−	2.10787i	24.2988				0		−21.4609	+	37.1713i
80.17	−1.97161				0		−4.11277			−9.03637	+	15.6514i		0		14.4807	−	8.36045i	23.8816				0		17.8162	−	30.8585i
80.18	−0.974030				0		−7.05127			3.52074	−	6.09810i		0		−8.62429	+	4.97924i	14.6604				0		−3.42931	+	5.93973i
80.19	−0.873662				0		−7.23671			−2.53659	+	4.39350i		0		−26.9512	+	15.5603i	13.3117				0		2.21612	−	3.83843i
80.20	−0.813803				0		−7.33772			10.6090	−	18.3754i		0		−17.3555	+	10.0202i	12.4819				0		−8.63367	+	14.9540i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
43.d	odd	6	1	inner
129.h	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	387.4.t.a	✓	88
3.b	odd	2	1	inner	387.4.t.a	✓	88
43.d	odd	6	1	inner	387.4.t.a	✓	88
129.h	even	6	1	inner	387.4.t.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
387.4.t.a	✓	88	1.a	even	1	1	trivial
387.4.t.a	✓	88	3.b	odd	2	1	inner
387.4.t.a	✓	88	43.d	odd	6	1	inner
387.4.t.a	✓	88	129.h	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(387, [\chi])\).