Newform orbit 91.5.b.c

• Label: 91.5.b.c
• Level: $91$
• Weight: $5$
• Character orbit: 91.b
• Analytic conductor: $9.407$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	91.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.40666664063\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 260 q^{4} - 936 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
90.1		−	7.29035i		−	8.59396i	−37.1492			3.32237			−62.6530			−31.2319	+	37.7567i			154.185i	7.14378				−	24.2213i
90.2		−	7.29035i			8.59396i	−37.1492			−3.32237			62.6530			31.2319	+	37.7567i			154.185i	7.14378					24.2213i
90.3		−	6.62243i		−	3.62781i	−27.8566			−35.6458			−24.0249			−11.4340	−	47.6473i			78.5198i	67.8390					236.062i
90.4		−	6.62243i			3.62781i	−27.8566			35.6458			24.0249			11.4340	−	47.6473i			78.5198i	67.8390				−	236.062i
90.5		−	5.90557i		−	15.8634i	−18.8758			−16.2792			−93.6825			48.9421	−	2.38147i			16.9833i	−170.647					96.1381i
90.6		−	5.90557i			15.8634i	−18.8758			16.2792			93.6825			−48.9421	−	2.38147i			16.9833i	−170.647				−	96.1381i
90.7		−	4.98341i		−	14.1593i	−8.83439			37.2024			−70.5614			−46.1652	−	16.4247i		−	35.7092i	−119.484				−	185.395i
90.8		−	4.98341i			14.1593i	−8.83439			−37.2024			70.5614			46.1652	−	16.4247i		−	35.7092i	−119.484					185.395i
90.9		−	4.01321i		−	2.72957i	−0.105892			30.9572			−10.9544			20.4779	+	44.5158i		−	63.7865i	73.5494				−	124.238i
90.10		−	4.01321i			2.72957i	−0.105892			−30.9572			10.9544			−20.4779	+	44.5158i		−	63.7865i	73.5494					124.238i
90.11		−	3.89234i		−	5.83401i	0.849652			8.73225			−22.7080			48.8772	+	3.46667i		−	65.5847i	46.9643				−	33.9889i
90.12		−	3.89234i			5.83401i	0.849652			−8.73225			22.7080			−48.8772	+	3.46667i		−	65.5847i	46.9643					33.9889i
90.13		−	1.65881i		−	14.8245i	13.2484			−32.1514			−24.5910			−36.6363	+	32.5389i		−	48.5173i	−138.767					53.3330i
90.14		−	1.65881i			14.8245i	13.2484			32.1514			24.5910			36.6363	+	32.5389i		−	48.5173i	−138.767				−	53.3330i
90.15		−	1.50866i		−	9.03315i	13.7240			−9.79747			−13.6279			−9.82211	−	48.0055i		−	44.8433i	−0.597837					14.7810i
90.16		−	1.50866i			9.03315i	13.7240			9.79747			13.6279			9.82211	−	48.0055i		−	44.8433i	−0.597837				−	14.7810i
90.17			1.50866i		−	9.03315i	13.7240			9.79747			13.6279			9.82211	+	48.0055i			44.8433i	−0.597837					14.7810i
90.18			1.50866i			9.03315i	13.7240			−9.79747			−13.6279			−9.82211	+	48.0055i			44.8433i	−0.597837				−	14.7810i
90.19			1.65881i		−	14.8245i	13.2484			32.1514			24.5910			36.6363	−	32.5389i			48.5173i	−138.767					53.3330i
90.20			1.65881i			14.8245i	13.2484			−32.1514			−24.5910			−36.6363	−	32.5389i			48.5173i	−138.767				−	53.3330i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
13.b	even	2	1	inner
91.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.5.b.c	✓	32
7.b	odd	2	1	inner	91.5.b.c	✓	32
13.b	even	2	1	inner	91.5.b.c	✓	32
91.b	odd	2	1	inner	91.5.b.c	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.5.b.c	✓	32	1.a	even	1	1	trivial
91.5.b.c	✓	32	7.b	odd	2	1	inner
91.5.b.c	✓	32	13.b	even	2	1	inner
91.5.b.c	✓	32	91.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{5}^{\mathrm{new}}(91, [\chi])\):

T2^16 + 193*T2^14 + 15083*T2^12 + 614639*T2^10 + 14004332*T2^8 + 177216104*T2^6 + 1153782320*T2^4 + 3213065904*T2^2 + 3085248448

T5^16 - 5095*T5^14 + 10178324*T5^12 - 10007225154*T5^10 + 4967789425189*T5^8 - 1155821879264095*T5^6 + 116336895811028022*T5^4 - 4529180914721543912*T5^2 + 37301594947130036224