Newform orbit 381.2.g.c

• Label: 381.2.g.c
• Level: $381$
• Weight: $2$
• Character orbit: 381.g
• Analytic conductor: $3.042$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.04230031701\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 72 q^{4} - 9 q^{6} - 6 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
20.1		−	2.71445i	−0.518986	−	1.65247i	−5.36824			0.893206			−4.48554	+	1.40876i	−1.99265	+	1.15046i			9.14292i	−2.46131	+	1.71522i		−	2.42456i
20.2		−	2.52018i	1.72695	+	0.132856i	−4.35132			2.75121			0.334820	−	4.35222i	−0.393176	+	0.227000i			5.92576i	2.96470	+	0.458869i		−	6.93355i
20.3		−	2.51015i	−0.291859	+	1.70728i	−4.30086			−1.12928			4.28554	+	0.732611i	4.45267	−	2.57075i			5.77550i	−2.82964	−	0.996573i			2.83467i
20.4		−	2.41695i	0.744448	+	1.56390i	−3.84163			−1.78400			3.77987	−	1.79929i	−3.12854	+	1.80626i			4.45113i	−1.89159	+	2.32849i			4.31183i
20.5		−	2.23119i	0.884630	−	1.48910i	−2.97822			0.125754			−3.32248	−	1.97378i	2.84593	−	1.64310i			2.18260i	−1.43486	−	2.63461i		−	0.280582i
20.6		−	2.19154i	−1.72917	−	0.0998148i	−2.80283			2.88844			−0.218748	+	3.78954i	2.87116	−	1.65766i			1.75944i	2.98007	+	0.345194i		−	6.33013i
20.7		−	2.18507i	−1.45123	−	0.945478i	−2.77451			−4.24066			−2.06593	+	3.17104i	1.53870	−	0.888369i			1.69237i	1.21214	+	2.74421i			9.26613i
20.8		−	1.92695i	1.25735	−	1.19125i	−1.71313			−2.87921			−2.29547	−	2.42285i	−3.83327	+	2.21314i		−	0.552789i	0.161862	−	2.99563i			5.54808i
20.9		−	1.50929i	−1.20481	+	1.24436i	−0.277965			−1.72647			1.87811	+	1.81841i	−0.611156	+	0.352851i		−	2.59905i	−0.0968780	−	2.99844i			2.60575i
20.10		−	1.44130i	−0.773084	+	1.54995i	−0.0773408			1.69273			2.23394	+	1.11424i	−1.09077	+	0.629759i		−	2.77113i	−1.80468	−	2.39648i		−	2.43973i
20.11		−	1.39140i	1.66784	+	0.467248i	0.0640060			−2.84814			0.650129	−	2.32063i	2.53428	−	1.46316i		−	2.87186i	2.56336	+	1.55859i			3.96290i
20.12		−	1.23123i	0.393008	−	1.68687i	0.484071			4.31193			−2.07693	−	0.483883i	−2.81895	+	1.62752i		−	3.05846i	−2.69109	−	1.32591i		−	5.30898i
20.13		−	1.06432i	−0.232359	−	1.71639i	0.867231			−0.493663			−1.82679	+	0.247304i	1.71308	−	0.989047i		−	3.05164i	−2.89202	+	0.797640i			0.525413i
20.14		−	0.644462i	−1.66095	−	0.491155i	1.58467			−1.85134			−0.316531	+	1.07042i	−4.13935	+	2.38985i		−	2.31018i	2.51753	+	1.63157i			1.19312i
20.15		−	0.526296i	1.69800	−	0.341774i	1.72301			−0.00872515			−0.179874	−	0.893648i	−0.609981	+	0.352173i		−	1.95941i	2.76638	−	1.16066i			0.00459201i
20.16		−	0.367913i	1.19765	+	1.25126i	1.86464			2.77415			0.460353	−	0.440630i	−3.10329	+	1.79168i		−	1.42185i	−0.131284	+	2.99713i		−	1.02065i
20.17		−	0.314327i	−1.34652	−	1.08944i	1.90120			1.52320			−0.342441	+	0.423247i	2.18809	−	1.26330i		−	1.22625i	0.626226	+	2.93391i		−	0.478781i
20.18		−	0.0526567i	−1.62710	+	0.593763i	1.99723			−3.05043			0.0312656	+	0.0856775i	2.07723	−	1.19929i		−	0.210481i	2.29489	−	1.93222i			0.160626i
20.19			0.0526567i	−1.32776	+	1.11223i	1.99723			3.05043			−0.0585661	−	0.0699155i	2.07723	−	1.19929i			0.210481i	0.525907	−	2.95354i			0.160626i
20.20			0.314327i	0.270226	+	1.71084i	1.90120			−1.52320			−0.537763	+	0.0849394i	2.18809	−	1.26330i			1.22625i	−2.85396	+	0.924629i		−	0.478781i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
127.d	odd	6	1	inner
381.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	381.2.g.c	✓	72
3.b	odd	2	1	inner	381.2.g.c	✓	72
127.d	odd	6	1	inner	381.2.g.c	✓	72
381.g	even	6	1	inner	381.2.g.c	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
381.2.g.c	✓	72	1.a	even	1	1	trivial
381.2.g.c	✓	72	3.b	odd	2	1	inner
381.2.g.c	✓	72	127.d	odd	6	1	inner
381.2.g.c	✓	72	381.g	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(381, [\chi])\):

T2^36 + 54*T2^34 + 1323*T2^32 + 19465*T2^30 + 191861*T2^28 + 1338395*T2^26 + 6805950*T2^24 + 25608646*T2^22 + 71643666*T2^20 + 148518410*T2^18 + 225561591*T2^16 + 245963911*T2^14 + 186691821*T2^12 + 94304778*T2^10 + 29807181*T2^8 + 5444663*T2^6 + 509995*T2^4 + 19045*T2^2 + 49

T5^36 - 103*T5^34 + 4743*T5^32 - 129540*T5^30 + 2346705*T5^28 - 29859989*T5^26 + 275530396*T5^24 - 1876007657*T5^22 + 9495136355*T5^20 - 35703699119*T5^18 + 98920397779*T5^16 - 198528791325*T5^14 + 280435144563*T5^12 - 266095770894*T5^10 + 156901034448*T5^8 - 49868000973*T5^6 + 6203796561*T5^4 - 86655501*T5^2 + 6561