Newform orbit 91.8.i.a

• Label: 91.8.i.a
• Level: $91$
• Weight: $8$
• Character orbit: 91.i
• Analytic conductor: $28.427$
• Analytic rank: $0$
• Dimension: $124$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(28.4270373191\)
Analytic rank:	\(0\)
Dimension:	\(124\)
Relative dimension:	\(62\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 124 q - 4 q^{2} + 1056 q^{7} + 508 q^{8} - 78740 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
34.1	−14.7934	−	14.7934i		−	10.1597i			309.691i	−192.710	+	192.710i	−150.297	+	150.297i	−889.863	+	178.007i	2687.84	−	2687.84i	2083.78			5701.68
34.2	−14.7934	−	14.7934i			10.1597i			309.691i	192.710	−	192.710i	150.297	−	150.297i	−178.007	+	889.863i	2687.84	−	2687.84i	2083.78			−5701.68
34.3	−14.7633	−	14.7633i		−	49.4145i			307.909i	−171.498	+	171.498i	−729.520	+	729.520i	645.680	−	637.683i	2656.06	−	2656.06i	−254.792			5063.74
34.4	−14.7633	−	14.7633i			49.4145i			307.909i	171.498	−	171.498i	729.520	−	729.520i	637.683	−	645.680i	2656.06	−	2656.06i	−254.792			−5063.74
34.5	−14.1673	−	14.1673i		−	73.8913i			273.425i	166.711	−	166.711i	−1046.84	+	1046.84i	427.412	+	800.539i	2060.29	−	2060.29i	−3272.93			−4723.70
34.6	−14.1673	−	14.1673i			73.8913i			273.425i	−166.711	+	166.711i	1046.84	−	1046.84i	−800.539	−	427.412i	2060.29	−	2060.29i	−3272.93			4723.70
34.7	−13.1108	−	13.1108i		−	69.2720i			215.788i	190.851	−	190.851i	−908.213	+	908.213i	−518.560	−	744.741i	1150.97	−	1150.97i	−2611.60			−5004.43
34.8	−13.1108	−	13.1108i			69.2720i			215.788i	−190.851	+	190.851i	908.213	−	908.213i	744.741	+	518.560i	1150.97	−	1150.97i	−2611.60			5004.43
34.9	−11.6264	−	11.6264i		−	4.85091i			142.349i	−312.712	+	312.712i	−56.3989	+	56.3989i	486.463	+	766.092i	166.822	−	166.822i	2163.47			7271.46
34.10	−11.6264	−	11.6264i			4.85091i			142.349i	312.712	−	312.712i	56.3989	−	56.3989i	−766.092	−	486.463i	166.822	−	166.822i	2163.47			−7271.46
34.11	−10.4745	−	10.4745i		−	72.1133i			91.4302i	−135.243	+	135.243i	−755.351	+	755.351i	−864.013	+	277.532i	−383.050	+	383.050i	−3013.33			2833.21
34.12	−10.4745	−	10.4745i			72.1133i			91.4302i	135.243	−	135.243i	755.351	−	755.351i	−277.532	+	864.013i	−383.050	+	383.050i	−3013.33			−2833.21
34.13	−10.2581	−	10.2581i		−	10.2312i			82.4578i	−92.8579	+	92.8579i	−104.953	+	104.953i	148.067	−	895.332i	−467.177	+	467.177i	2082.32			1905.09
34.14	−10.2581	−	10.2581i			10.2312i			82.4578i	92.8579	−	92.8579i	104.953	−	104.953i	895.332	−	148.067i	−467.177	+	467.177i	2082.32			−1905.09
34.15	−10.2031	−	10.2031i		−	45.2869i			80.2048i	250.342	−	250.342i	−462.065	+	462.065i	827.941	+	371.561i	−487.657	+	487.657i	136.094			−5108.50
34.16	−10.2031	−	10.2031i			45.2869i			80.2048i	−250.342	+	250.342i	462.065	−	462.065i	−371.561	−	827.941i	−487.657	+	487.657i	136.094			5108.50
34.17	−7.63468	−	7.63468i		−	86.4411i		−	11.4232i	−332.270	+	332.270i	−659.951	+	659.951i	882.530	−	211.385i	−1064.45	+	1064.45i	−5285.06			5073.56
34.18	−7.63468	−	7.63468i			86.4411i		−	11.4232i	332.270	−	332.270i	659.951	−	659.951i	211.385	−	882.530i	−1064.45	+	1064.45i	−5285.06			−5073.56
34.19	−7.17834	−	7.17834i		−	37.6656i		−	24.9429i	−15.3466	+	15.3466i	−270.376	+	270.376i	−83.6049	+	903.633i	−1097.88	+	1097.88i	768.304			220.326
34.20	−7.17834	−	7.17834i			37.6656i		−	24.9429i	15.3466	−	15.3466i	270.376	−	270.376i	−903.633	+	83.6049i	−1097.88	+	1097.88i	768.304			−220.326

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
13.d	odd	4	1	inner
91.i	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.8.i.a	✓	124
7.b	odd	2	1	inner	91.8.i.a	✓	124
13.d	odd	4	1	inner	91.8.i.a	✓	124
91.i	even	4	1	inner	91.8.i.a	✓	124

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.8.i.a	✓	124	1.a	even	1	1	trivial
91.8.i.a	✓	124	7.b	odd	2	1	inner
91.8.i.a	✓	124	13.d	odd	4	1	inner
91.8.i.a	✓	124	91.i	even	4	1	inner

Hecke kernels

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