Newform orbit 92.6.b.b

• Label: 92.6.b.b
• Level: $92$
• Weight: $6$
• Character orbit: 92.b
• Analytic conductor: $14.755$
• Analytic rank: $0$
• Dimension: $52$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	92.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7553114228\)
Analytic rank:	\(0\)
Dimension:	\(52\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q + 40 q^{4} + 752 q^{6} - 24 q^{8} - 2920 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
91.1	−5.65179	−	0.239233i			26.3120i	31.8855	+	2.70419i		−	61.1744i	6.29471	−	148.710i	202.685			−179.564	−	22.9116i	−449.323			−14.6349	+	345.745i
91.2	−5.65179	−	0.239233i			26.3120i	31.8855	+	2.70419i			61.1744i	6.29471	−	148.710i	−202.685			−179.564	−	22.9116i	−449.323			14.6349	−	345.745i
91.3	−5.65179	+	0.239233i		−	26.3120i	31.8855	−	2.70419i		−	61.1744i	6.29471	+	148.710i	−202.685			−179.564	+	22.9116i	−449.323			14.6349	+	345.745i
91.4	−5.65179	+	0.239233i		−	26.3120i	31.8855	−	2.70419i			61.1744i	6.29471	+	148.710i	202.685			−179.564	+	22.9116i	−449.323			−14.6349	−	345.745i
91.5	−5.46870	−	1.44683i		−	10.3194i	27.8133	+	15.8246i		−	69.5061i	−14.9304	+	56.4336i	143.670			−129.207	−	126.781i	136.510			−100.564	+	380.108i
91.6	−5.46870	−	1.44683i		−	10.3194i	27.8133	+	15.8246i			69.5061i	−14.9304	+	56.4336i	−143.670			−129.207	−	126.781i	136.510			100.564	−	380.108i
91.7	−5.46870	+	1.44683i			10.3194i	27.8133	−	15.8246i		−	69.5061i	−14.9304	−	56.4336i	−143.670			−129.207	+	126.781i	136.510			100.564	+	380.108i
91.8	−5.46870	+	1.44683i			10.3194i	27.8133	−	15.8246i			69.5061i	−14.9304	−	56.4336i	143.670			−129.207	+	126.781i	136.510			−100.564	−	380.108i
91.9	−4.25930	−	3.72268i			21.3436i	4.28326	+	31.7120i		−	34.2809i	79.4555	−	90.9089i	−167.350			99.8102	−	151.016i	−212.550			−127.617	+	146.013i
91.10	−4.25930	−	3.72268i			21.3436i	4.28326	+	31.7120i			34.2809i	79.4555	−	90.9089i	167.350			99.8102	−	151.016i	−212.550			127.617	−	146.013i
91.11	−4.25930	+	3.72268i		−	21.3436i	4.28326	−	31.7120i		−	34.2809i	79.4555	+	90.9089i	167.350			99.8102	+	151.016i	−212.550			127.617	+	146.013i
91.12	−4.25930	+	3.72268i		−	21.3436i	4.28326	−	31.7120i			34.2809i	79.4555	+	90.9089i	−167.350			99.8102	+	151.016i	−212.550			−127.617	−	146.013i
91.13	−3.75744	−	4.22867i		−	22.2487i	−3.76326	+	31.7779i		−	58.3034i	−94.0826	+	83.5984i	−26.0697			148.519	−	103.490i	−252.007			−246.546	+	219.072i
91.14	−3.75744	−	4.22867i		−	22.2487i	−3.76326	+	31.7779i			58.3034i	−94.0826	+	83.5984i	26.0697			148.519	−	103.490i	−252.007			246.546	−	219.072i
91.15	−3.75744	+	4.22867i			22.2487i	−3.76326	−	31.7779i		−	58.3034i	−94.0826	−	83.5984i	26.0697			148.519	+	103.490i	−252.007			246.546	+	219.072i
91.16	−3.75744	+	4.22867i			22.2487i	−3.76326	−	31.7779i			58.3034i	−94.0826	−	83.5984i	−26.0697			148.519	+	103.490i	−252.007			−246.546	−	219.072i
91.17	−3.18270	−	4.67658i			6.14208i	−11.7408	+	29.7683i		−	90.1541i	28.7239	−	19.5484i	−60.2020			176.582	−	39.8367i	205.275			−421.613	+	286.933i
91.18	−3.18270	−	4.67658i			6.14208i	−11.7408	+	29.7683i			90.1541i	28.7239	−	19.5484i	60.2020			176.582	−	39.8367i	205.275			421.613	−	286.933i
91.19	−3.18270	+	4.67658i		−	6.14208i	−11.7408	−	29.7683i		−	90.1541i	28.7239	+	19.5484i	60.2020			176.582	+	39.8367i	205.275			421.613	+	286.933i
91.20	−3.18270	+	4.67658i		−	6.14208i	−11.7408	−	29.7683i			90.1541i	28.7239	+	19.5484i	−60.2020			176.582	+	39.8367i	205.275			−421.613	−	286.933i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
23.b	odd	2	1	inner
92.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.6.b.b	✓	52
4.b	odd	2	1	inner	92.6.b.b	✓	52
23.b	odd	2	1	inner	92.6.b.b	✓	52
92.b	even	2	1	inner	92.6.b.b	✓	52

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.6.b.b	✓	52	1.a	even	1	1	trivial
92.6.b.b	✓	52	4.b	odd	2	1	inner
92.6.b.b	✓	52	23.b	odd	2	1	inner
92.6.b.b	✓	52	92.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^26 + 3889*T3^24 + 6525612*T3^22 + 6216820220*T3^20 + 3726762236390*T3^18 + 1474655491887750*T3^16 + 393957450937677628*T3^14 + 71640006711399946396*T3^12 + 8843928019841809784097*T3^10 + 730662816139995753170001*T3^8 + 39197269015846700994493200*T3^6 + 1290649918529609327024269920*T3^4 + 23360288253082721742726153216*T3^2 + 175599640522061142774349033728