Newform orbit 224.6.p.a

• Label: 224.6.p.a
• Level: $224$
• Weight: $6$
• Character orbit: 224.p
• Analytic conductor: $35.926$
• Analytic rank: $0$
• Dimension: $80$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(35.9259756381\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(40\) 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.

\(\operatorname{Tr}(f)(q) = \) 80 * q - 3240 * q^9 + 6856 * q^21 + 27728 * q^25 - 15920 * q^29 - 28296 * q^33 - 2152 * q^37 + 35400 * q^45 + 29280 * q^49 - 17512 * q^53 - 108368 * q^57 + 37704 * q^61 + 18216 * q^65 + 157704 * q^73 + 28224 * q^77 - 273136 * q^81 + 230704 * q^85 + 28440 * q^89 + 39400 * q^93

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
31.1		0		−14.5286	+	25.1643i		0		−52.7981	+	30.4830i		0		−118.674	−	52.1868i		0		−300.662	−	520.762i		0
31.2		0		−14.1595	+	24.5249i		0		74.7559	−	43.1604i		0		−13.7127	−	128.915i		0		−279.481	−	484.075i		0
31.3		0		−14.0954	+	24.4139i		0		−20.5199	+	11.8471i		0		122.094	−	43.5908i		0		−275.859	−	477.802i		0
31.4		0		−12.7076	+	22.0102i		0		31.1638	−	17.9924i		0		69.5584	+	109.401i		0		−201.466	−	348.949i		0
31.5		0		−12.3958	+	21.4701i		0		−52.5633	+	30.3474i		0		102.609	+	79.2362i		0		−185.811	−	321.834i		0
31.6		0		−10.6026	+	18.3643i		0		−46.1752	+	26.6593i		0		−106.089	+	74.5124i		0		−103.332	−	178.976i		0
31.7		0		−10.3078	+	17.8537i		0		74.8496	−	43.2144i		0		−129.604	−	3.12192i		0		−91.0020	−	157.620i		0
31.8		0		−9.84215	+	17.0471i		0		51.5533	−	29.7643i		0		−27.6862	+	126.651i		0		−72.2357	−	125.116i		0
31.9		0		−9.26714	+	16.0512i		0		22.9226	−	13.2343i		0		−73.0552	−	107.098i		0		−50.2597	−	87.0523i		0
31.10		0		−8.95676	+	15.5136i		0		−94.4708	+	54.5427i		0		65.8412	−	111.678i		0		−38.9472	−	67.4586i		0
31.11		0		−8.16376	+	14.1401i		0		19.2452	−	11.1112i		0		103.004	−	78.7217i		0		−11.7941	−	20.4280i		0
31.12		0		−7.38571	+	12.7924i		0		−16.6824	+	9.63157i		0		−103.628	+	77.8993i		0		12.4026	+	21.4819i		0
31.13		0		−4.79182	+	8.29968i		0		−38.1493	+	22.0255i		0		−61.1737	−	114.301i		0		75.5769	+	130.903i		0
31.14		0		−4.31061	+	7.46619i		0		4.69276	−	2.70937i		0		26.3019	−	126.946i		0		84.3373	+	146.077i		0
31.15		0		−4.02257	+	6.96730i		0		−41.2433	+	23.8118i		0		−79.3382	+	102.530i		0		89.1379	+	154.391i		0
31.16		0		−3.76024	+	6.51293i		0		−83.0525	+	47.9504i		0		105.609	+	75.1911i		0		93.2211	+	161.464i		0
31.17		0		−3.39807	+	5.88563i		0		46.3722	−	26.7730i		0		128.116	+	19.8289i		0		98.4062	+	170.445i		0
31.18		0		−2.65686	+	4.60182i		0		81.1102	−	46.8290i		0		59.3664	+	115.250i		0		107.382	+	185.991i		0
31.19		0		−1.05307	+	1.82396i		0		67.8945	−	39.1989i		0		121.710	−	44.6500i		0		119.282	+	206.603i		0
31.20		0		−0.445224	+	0.771150i		0		−28.9053	+	16.6885i		0		103.498	+	78.0719i		0		121.104	+	209.758i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.d	odd	6	1	inner
28.f	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	224.6.p.a	✓	80
4.b	odd	2	1	inner	224.6.p.a	✓	80
7.d	odd	6	1	inner	224.6.p.a	✓	80
28.f	even	6	1	inner	224.6.p.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
224.6.p.a	✓	80	1.a	even	1	1	trivial
224.6.p.a	✓	80	4.b	odd	2	1	inner
224.6.p.a	✓	80	7.d	odd	6	1	inner
224.6.p.a	✓	80	28.f	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(224, [\chi])\).