Newform orbit 91.8.c.a

• Label: 91.8.c.a
• Level: $91$
• Weight: $8$
• Character orbit: 91.c
• Analytic conductor: $28.427$
• Analytic rank: $0$
• Dimension: $50$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(28.4270373191\)
Analytic rank:	\(0\)
Dimension:	\(50\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
64.1		−	22.2828i	−16.8313			−368.522					186.348i			375.049i			343.000i			5359.48i	−1903.71			4152.34
64.2		−	21.0014i	55.1097			−313.061					298.534i		−	1157.38i		−	343.000i			3886.54i	850.082			6269.64
64.3		−	20.4516i	−67.6652			−290.269					268.414i			1383.86i		−	343.000i			3318.67i	2391.58			5489.50
64.4		−	20.3011i	50.0015			−284.134				−	340.641i		−	1015.08i			343.000i			3169.69i	313.148			−6915.39
64.5		−	20.0790i	−84.8054			−275.166				−	538.452i			1702.81i			343.000i			2954.94i	5004.96			−10811.6
64.6		−	19.2961i	46.7043			−244.338				−	300.001i		−	901.208i		−	343.000i			2244.87i	−5.71295			−5788.83
64.7		−	17.7532i	−30.0870			−187.174				−	248.659i			534.138i		−	343.000i			1050.53i	−1281.77			−4414.48
64.8		−	16.9891i	92.8773			−160.631					107.578i		−	1577.91i			343.000i			554.371i	6439.20			1827.67
64.9		−	15.7347i	36.7387			−119.582					452.285i		−	578.073i			343.000i		−	132.453i	−837.271			7116.58
64.10		−	15.4646i	−2.30214			−111.152					85.0277i			35.6015i			343.000i		−	260.539i	−2181.70			1314.92
64.11		−	15.1105i	24.8832			−100.328					394.355i		−	375.998i		−	343.000i		−	418.137i	−1567.83			5958.92
64.12		−	14.7173i	−70.7615			−88.5983					406.740i			1041.42i			343.000i		−	579.886i	2820.20			5986.11
64.13		−	12.6128i	−83.1101			−31.0818					6.92246i			1048.25i		−	343.000i		−	1222.41i	4720.29			87.3113
64.14		−	11.3642i	31.8809			−1.14421				−	405.714i		−	362.299i			343.000i		−	1441.61i	−1170.61			−4610.60
64.15		−	11.0195i	−52.4283			6.57091				−	215.435i			577.733i			343.000i		−	1482.90i	561.727			−2373.98
64.16		−	10.6365i	74.1121			14.8657				−	114.172i		−	788.291i		−	343.000i		−	1519.59i	3305.61			−1214.39
64.17		−	9.69261i	−28.8717			34.0534					266.481i			279.842i		−	343.000i		−	1570.72i	−1353.43			2582.90
64.18		−	8.36017i	−8.01801			58.1075				−	455.948i			67.0319i		−	343.000i		−	1555.89i	−2122.71			−3811.80
64.19		−	5.70969i	−8.30892			95.3995					279.609i			47.4413i		−	343.000i		−	1275.54i	−2117.96			1596.48
64.20		−	4.39578i	−84.2461			108.677				−	187.956i			370.327i		−	343.000i		−	1040.38i	4910.40			−826.214

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.8.c.a	✓	50
13.b	even	2	1	inner	91.8.c.a	✓	50

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.8.c.a	✓	50	1.a	even	1	1	trivial
91.8.c.a	✓	50	13.b	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{8}^{\mathrm{new}}(91, [\chi])\).