Newform orbit 96.5.p.a

• Label: 96.5.p.a
• Level: $96$
• Weight: $5$
• Character orbit: 96.p
• Analytic conductor: $9.924$
• Analytic rank: $0$
• Dimension: $248$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	96.p (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.92351645605\)
Analytic rank:	\(0\)
Dimension:	\(248\)
Relative dimension:	\(62\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 248 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−3.99568	−	0.185808i	6.88111	−	5.80089i	15.9310	+	1.48486i	12.1262	−	29.2751i	−28.5726	+	21.8999i	−50.6402	−	50.6402i	−63.3791	−	8.89310i	13.6994	−	79.8331i	−53.8918	+	114.721i
5.2	−3.98973	−	0.286445i	−7.27242	+	5.30207i	15.8359	+	2.28568i	1.03929	−	2.50907i	30.5337	−	19.0707i	−13.2001	−	13.2001i	−62.5262	−	13.6553i	24.7760	−	77.1178i	−4.86520	+	9.71280i
5.3	−3.95130	+	0.622306i	8.32544	+	3.41864i	15.2255	−	4.91783i	−16.1290	+	38.9389i	−35.0237	−	8.32709i	−56.6723	−	56.6723i	−57.0999	+	28.9067i	57.6258	+	56.9233i	39.4987	−	163.896i
5.4	−3.93872	−	0.697470i	−6.83226	−	5.85835i	15.0271	+	5.49428i	17.4566	−	42.1439i	22.8244	+	27.8397i	58.4887	+	58.4887i	−55.3554	−	32.1214i	12.3596	+	80.0515i	−98.1506	+	153.818i
5.5	−3.93565	+	0.714623i	0.885807	+	8.95630i	14.9786	−	5.62500i	−7.05456	+	17.0312i	−9.88660	−	34.6158i	40.7944	+	40.7944i	−54.9308	+	32.8421i	−79.4307	+	15.8671i	15.5934	−	72.0702i
5.6	−3.80054	+	1.24736i	−2.06069	−	8.76091i	12.8882	−	9.48131i	−7.81621	+	18.8700i	18.7598	+	30.7257i	−6.44670	−	6.44670i	−37.1553	+	52.1103i	−72.5071	+	36.1070i	6.16803	−	81.4658i
5.7	−3.66509	+	1.60222i	2.57157	+	8.62479i	10.8658	−	11.7446i	16.0988	−	38.8660i	−23.2439	−	27.4904i	−5.38169	−	5.38169i	−21.0065	+	60.4543i	−67.7741	+	44.3585i	3.26838	+	168.241i
5.8	−3.65302	−	1.62955i	2.58774	−	8.61995i	10.6892	+	11.9055i	−2.37119	+	5.72455i	−23.4997	+	27.2720i	6.96147	+	6.96147i	−19.6471	−	60.9097i	−67.6072	−	44.6124i	17.9904	−	17.0480i
5.9	−3.65028	−	1.63569i	8.46217	+	3.06458i	10.6490	+	11.9414i	−0.344704	+	0.832190i	−25.8766	−	25.0281i	38.0513	+	38.0513i	−19.3394	−	61.0081i	62.2167	+	51.8660i	2.61947	−	2.47389i
5.10	−3.63883	−	1.66100i	−8.50797	−	2.93503i	10.4821	+	12.0882i	−14.5102	+	35.0307i	26.0840	+	24.8118i	−5.40232	−	5.40232i	−18.0642	−	61.3978i	63.7711	+	49.9424i	110.986	−	103.369i
5.11	−3.57187	+	1.80049i	8.19688	−	3.71633i	9.51648	−	12.8622i	2.80377	−	6.76890i	−22.5870	+	28.0326i	40.6004	+	40.6004i	−10.8333	+	63.0765i	53.3778	−	60.9246i	2.17263	+	29.2258i
5.12	−3.38708	+	2.12784i	−8.80311	−	1.87223i	6.94457	−	14.4143i	7.72872	−	18.6588i	33.8006	−	12.3903i	−44.0090	−	44.0090i	7.14967	+	63.5994i	73.9895	+	32.9628i	13.5252	+	79.6442i
5.13	−3.36288	−	2.16589i	2.72200	+	8.57850i	6.61787	+	14.5672i	7.74524	−	18.6987i	9.42629	−	34.7440i	−31.9932	−	31.9932i	9.29584	−	63.3213i	−66.1814	+	46.7014i	−66.5455	+	46.1060i
5.14	−3.06077	+	2.57520i	−8.99933	+	0.109420i	2.73668	−	15.7642i	−7.76155	+	18.7380i	27.2632	−	23.5100i	63.8392	+	63.8392i	32.2197	+	55.2982i	80.9761	−	1.96942i	−24.4979	−	77.3404i
5.15	−2.54409	−	3.08668i	−6.14135	−	6.57905i	−3.05517	+	15.7056i	7.64689	−	18.4612i	−4.68324	+	35.6941i	−66.0063	−	66.0063i	56.2508	−	30.5262i	−5.56771	+	80.8084i	−76.4383	+	23.3636i
5.16	−2.47960	−	3.13872i	−6.99418	+	5.66404i	−3.70313	+	15.5656i	9.20903	−	22.2326i	35.1207	+	7.90820i	15.9812	+	15.9812i	58.0383	−	26.9733i	16.8372	−	79.2307i	−92.6166	+	26.2234i
5.17	−2.47593	+	3.14162i	−3.93485	+	8.09425i	−3.73957	−	15.5569i	−8.82457	+	21.3044i	−15.6867	−	32.4026i	−37.0213	−	37.0213i	58.1326	+	26.7693i	−50.0339	−	63.6994i	−45.0814	−	80.4716i
5.18	−2.45714	−	3.15634i	−1.77298	+	8.82363i	−3.92495	+	15.5111i	−17.6070	+	42.5070i	32.2068	−	16.0847i	28.2290	+	28.2290i	58.6025	−	25.7245i	−74.7131	−	31.2883i	177.429	−	48.8720i
5.19	−2.42375	−	3.18205i	8.05090	−	4.02281i	−4.25086	+	15.4250i	−11.3106	+	27.3063i	−32.3141	−	15.8681i	−25.3764	−	25.3764i	59.3861	−	23.8599i	48.6341	−	64.7744i	114.304	−	30.1926i
5.20	−2.39388	+	3.20458i	8.02762	+	4.06906i	−4.53866	−	15.3428i	3.87636	−	9.35836i	−32.2568	+	15.9843i	−12.0775	−	12.0775i	60.0321	+	22.1843i	47.8854	+	65.3298i	20.7101	+	34.8249i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
32.g	even	8	1	inner
96.p	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	96.5.p.a	✓	248
3.b	odd	2	1	inner	96.5.p.a	✓	248
32.g	even	8	1	inner	96.5.p.a	✓	248
96.p	odd	8	1	inner	96.5.p.a	✓	248

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.5.p.a	✓	248	1.a	even	1	1	trivial
96.5.p.a	✓	248	3.b	odd	2	1	inner
96.5.p.a	✓	248	32.g	even	8	1	inner
96.5.p.a	✓	248	96.p	odd	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(96, [\chi])\).