Newform orbit 92.6.e.a

• Label: 92.6.e.a
• Level: $92$
• Weight: $6$
• Character orbit: 92.e
• Analytic conductor: $14.755$
• Analytic rank: $0$
• Dimension: $100$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7553114228\)
Analytic rank:	\(0\)
Dimension:	\(100\)
Relative dimension:	\(10\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 100 q + 2 q^{3} - 86 q^{5} - 118 q^{7} - 368 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−19.4258	−	22.4185i		0		4.51442	+	31.3985i		0		−15.2523	+	33.3978i		0		−90.6474	+	630.467i		0
9.2		0		−12.4147	−	14.3273i		0		−9.42610	−	65.5599i		0		78.8855	−	172.735i		0		−16.5647	+	115.210i		0
9.3		0		−8.08445	−	9.32995i		0		1.31986	+	9.17981i		0		−51.4996	+	112.768i		0		12.8928	−	89.6716i		0
9.4		0		−6.40420	−	7.39084i		0		8.58273	+	59.6942i		0		0.418484	−	0.916353i		0		20.9718	−	145.862i		0
9.5		0		−3.49433	−	4.03267i		0		−12.4935	−	86.8940i		0		−77.3772	+	169.433i		0		30.5304	−	212.344i		0
9.6		0		4.37991	+	5.05468i		0		8.80161	+	61.2166i		0		104.926	−	229.755i		0		28.2163	−	196.249i		0
9.7		0		6.13010	+	7.07452i		0		−4.22072	−	29.3558i		0		−9.33879	+	20.4491i		0		22.1119	−	153.792i		0
9.8		0		10.4151	+	12.0197i		0		−8.44637	−	58.7458i		0		31.4224	−	68.8055i		0		−1.41556	+	9.84542i		0
9.9		0		11.4776	+	13.2458i		0		12.0436	+	83.7652i		0		−61.5718	+	134.823i		0		−9.13473	+	63.5334i		0
9.10		0		17.9648	+	20.7325i		0		−1.92175	−	13.3660i		0		−7.58868	+	16.6169i		0		−72.5192	+	504.382i		0
13.1		0		−21.4586	−	13.7906i		0		−33.5221	+	73.4031i		0		39.9406	+	11.7276i		0		169.344	+	370.813i		0
13.2		0		−19.5241	−	12.5474i		0		43.6628	−	95.6081i		0		189.239	+	55.5656i		0		122.808	+	268.913i		0
13.3		0		−16.2560	−	10.4471i		0		11.9826	−	26.2383i		0		−192.701	−	56.5820i		0		54.1699	+	118.615i		0
13.4		0		−7.14271	−	4.59034i		0		−4.30281	+	9.42183i		0		54.2959	+	15.9427i		0		−70.9988	−	155.466i		0
13.5		0		−1.31220	−	0.843300i		0		6.29170	−	13.7769i		0		82.6884	+	24.2795i		0		−99.9351	−	218.827i		0
13.6		0		5.11833	+	3.28935i		0		−27.3903	+	59.9763i		0		−164.862	−	48.4077i		0		−85.5683	−	187.369i		0
13.7		0		8.41459	+	5.40773i		0		36.4994	−	79.9225i		0		−123.792	−	36.3487i		0		−59.3840	−	130.033i		0
13.8		0		12.0305	+	7.73153i		0		−39.1925	+	85.8195i		0		137.896	+	40.4899i		0		−15.9897	−	35.0125i		0
13.9		0		17.5082	+	11.2518i		0		14.8856	−	32.5949i		0		107.901	+	31.6826i		0		78.9867	+	172.957i		0
13.10		0		24.2364	+	15.5758i		0		−11.6103	+	25.4230i		0		−177.640	−	52.1597i		0		243.851	+	533.960i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.6.e.a	✓	100
23.c	even	11	1	inner	92.6.e.a	✓	100

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.6.e.a	✓	100	1.a	even	1	1	trivial
92.6.e.a	✓	100	23.c	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{6}^{\mathrm{new}}(92, [\chi])\).