Newform orbit 192.10.c.e

• Label: 192.10.c.e
• Level: $192$
• Weight: $10$
• Character orbit: 192.c
• Analytic conductor: $98.887$
• Analytic rank: $0$
• Dimension: $36$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	192.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(98.8868805435\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 27740 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
191.1		0		−138.495	−	22.4067i		0				567.508i		0				2026.54i		0		18678.9	+	6206.44i		0
191.2		0		−138.495	+	22.4067i		0			−	567.508i		0			−	2026.54i		0		18678.9	−	6206.44i		0
191.3		0		−133.825	−	42.1174i		0			−	1154.74i		0				11809.8i		0		16135.2	+	11272.7i		0
191.4		0		−133.825	+	42.1174i		0				1154.74i		0			−	11809.8i		0		16135.2	−	11272.7i		0
191.5		0		−126.208	−	61.2753i		0			−	2229.78i		0			−	1688.34i		0		12173.7	+	15466.8i		0
191.6		0		−126.208	+	61.2753i		0				2229.78i		0				1688.34i		0		12173.7	−	15466.8i		0
191.7		0		−98.8573	−	99.5502i		0				2632.92i		0			−	2656.96i		0		−137.487	+	19682.5i		0
191.8		0		−98.8573	+	99.5502i		0			−	2632.92i		0				2656.96i		0		−137.487	−	19682.5i		0
191.9		0		−95.5235	−	102.753i		0				1651.15i		0				6595.07i		0		−1433.53	+	19630.7i		0
191.10		0		−95.5235	+	102.753i		0			−	1651.15i		0			−	6595.07i		0		−1433.53	−	19630.7i		0
191.11		0		−91.7180	−	106.164i		0			−	108.948i		0			−	8414.62i		0		−2858.64	+	19474.3i		0
191.12		0		−91.7180	+	106.164i		0				108.948i		0				8414.62i		0		−2858.64	−	19474.3i		0
191.13		0		−54.2425	−	129.386i		0			−	1370.73i		0			−	9846.02i		0		−13798.5	+	14036.5i		0
191.14		0		−54.2425	+	129.386i		0				1370.73i		0				9846.02i		0		−13798.5	−	14036.5i		0
191.15		0		−40.0507	−	134.458i		0			−	1314.15i		0				4845.60i		0		−16474.9	+	10770.3i		0
191.16		0		−40.0507	+	134.458i		0				1314.15i		0			−	4845.60i		0		−16474.9	−	10770.3i		0
191.17		0		−15.2190	−	139.468i		0				999.686i		0				3618.59i		0		−19219.8	+	4245.13i		0
191.18		0		−15.2190	+	139.468i		0			−	999.686i		0			−	3618.59i		0		−19219.8	−	4245.13i		0
191.19		0		15.2190	−	139.468i		0			−	999.686i		0				3618.59i		0		−19219.8	−	4245.13i		0
191.20		0		15.2190	+	139.468i		0				999.686i		0			−	3618.59i		0		−19219.8	+	4245.13i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
4.b	odd	2	1	inner
12.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	192.10.c.e		36
3.b	odd	2	1	inner	192.10.c.e		36
4.b	odd	2	1	inner	192.10.c.e		36
8.b	even	2	1		96.10.c.a	✓	36
8.d	odd	2	1		96.10.c.a	✓	36
12.b	even	2	1	inner	192.10.c.e		36
24.f	even	2	1		96.10.c.a	✓	36
24.h	odd	2	1		96.10.c.a	✓	36

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.10.c.a	✓	36	8.b	even	2	1
96.10.c.a	✓	36	8.d	odd	2	1
96.10.c.a	✓	36	24.f	even	2	1
96.10.c.a	✓	36	24.h	odd	2	1
192.10.c.e		36	1.a	even	1	1	trivial
192.10.c.e		36	3.b	odd	2	1	inner
192.10.c.e		36	4.b	odd	2	1	inner
192.10.c.e		36	12.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^18 + 20903112*T5^16 + 173668835996928*T5^14 + 749581594182635292672*T5^12 + 1844988565493271253712560128*T5^10 + 2653127445503944063460255147163648*T5^8 + 2163601323033328613528915846431899648000*T5^6 + 899324239597958798795590937259825341399040000*T5^4 + 141234564555710732121299278845604776284258304000000*T5^2 + 1553257448007659175972953439353184139931077836800000000