Newform orbit 48.7.l.a

• Label: 48.7.l.a
• Level: $48$
• Weight: $7$
• Character orbit: 48.l
• Analytic conductor: $11.043$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.0425960138\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−7.91026	+	1.19493i	11.0227	−	11.0227i	61.1443	−	18.9044i	156.277	−	156.277i	−74.0211	+	100.364i	23.3623			−461.078	+	222.601i		−	243.000i	−1049.45	+	1422.93i
19.2	−7.86116	−	1.48398i	−11.0227	+	11.0227i	59.5956	+	23.3316i	52.2146	−	52.2146i	103.009	−	70.2938i	−282.592			−433.867	−	271.852i		−	243.000i	−487.953	+	332.982i
19.3	−7.47563	+	2.84868i	−11.0227	+	11.0227i	47.7700	−	42.5914i	−55.7840	+	55.7840i	51.0014	−	113.802i	496.753			−235.781	+	454.479i		−	243.000i	258.109	−	575.931i
19.4	−7.29112	+	3.29235i	11.0227	−	11.0227i	42.3208	−	48.0099i	−73.3870	+	73.3870i	−44.0772	+	116.658i	291.401			−150.501	+	489.381i		−	243.000i	293.457	−	776.689i
19.5	−7.21738	−	3.45101i	11.0227	−	11.0227i	40.1811	+	49.8145i	−26.8357	+	26.8357i	−117.594	+	41.5155i	−81.4485			−118.092	−	498.195i		−	243.000i	286.294	−	101.073i
19.6	−5.74110	−	5.57133i	−11.0227	+	11.0227i	1.92050	+	63.9712i	−160.484	+	160.484i	124.694	−	1.87131i	−53.5181			345.379	−	377.965i		−	243.000i	1815.46	−	27.2451i
19.7	−4.50221	+	6.61288i	11.0227	−	11.0227i	−23.4602	−	59.5451i	−9.26689	+	9.26689i	23.2652	+	122.518i	−320.373			499.387	+	112.945i		−	243.000i	−19.5593	−	103.002i
19.8	−3.75499	−	7.06400i	−11.0227	+	11.0227i	−35.8001	+	53.0505i	107.837	−	107.837i	119.254	+	36.4742i	5.36994			509.177	+	53.6875i		−	243.000i	−1166.68	−	356.832i
19.9	−3.30175	+	7.28687i	−11.0227	+	11.0227i	−42.1969	−	48.1188i	−98.7574	+	98.7574i	−43.9268	−	116.715i	−218.381			489.959	−	148.607i		−	243.000i	−393.560	−	1045.70i
19.10	−2.85723	−	7.47236i	11.0227	−	11.0227i	−47.6725	+	42.7006i	−99.4317	+	99.4317i	−113.860	−	50.8712i	407.926			455.285	+	234.221i		−	243.000i	1027.09	+	458.891i
19.11	−0.382617	+	7.99085i	−11.0227	+	11.0227i	−63.7072	−	6.11486i	122.335	−	122.335i	−83.8632	−	92.2982i	392.292			73.2383	−	506.735i		−	243.000i	930.754	+	1024.37i
19.12	0.181149	+	7.99795i	11.0227	−	11.0227i	−63.9344	+	2.89763i	−124.587	+	124.587i	90.1558	+	86.1623i	200.172			−34.7567	−	510.819i		−	243.000i	−1019.01	−	973.874i
19.13	1.02416	−	7.93417i	11.0227	−	11.0227i	−61.9022	−	16.2518i	145.472	−	145.472i	−76.1670	−	98.7451i	535.877			−192.342	+	474.498i		−	243.000i	−1005.21	−	1303.19i
19.14	1.27618	+	7.89755i	11.0227	−	11.0227i	−60.7427	+	20.1574i	132.791	−	132.791i	101.119	+	72.9854i	−560.492			−236.713	−	453.995i		−	243.000i	1218.19	+	879.260i
19.15	1.61327	−	7.83565i	−11.0227	+	11.0227i	−58.7947	−	25.2820i	−15.5658	+	15.5658i	68.5874	+	104.153i	10.2991			−292.952	+	419.908i		−	243.000i	96.8564	+	147.080i
19.16	3.36544	−	7.25767i	11.0227	−	11.0227i	−41.3476	−	48.8505i	−26.6395	+	26.6395i	−42.9029	−	117.095i	−403.840			−493.694	+	135.684i		−	243.000i	103.687	+	282.994i
19.17	4.87132	+	6.34588i	−11.0227	+	11.0227i	−16.5404	+	61.8257i	−95.7535	+	95.7535i	−123.644	−	16.2536i	338.697			−472.912	+	196.210i		−	243.000i	−1074.09	−	141.194i
19.18	5.00967	+	6.23724i	−11.0227	+	11.0227i	−13.8064	+	62.4931i	45.7781	−	45.7781i	−123.971	−	13.5312i	−565.544			−458.950	+	226.956i		−	243.000i	514.863	+	56.1959i
19.19	5.29238	+	5.99922i	11.0227	−	11.0227i	−7.98136	+	63.5004i	47.0845	−	47.0845i	124.464	+	7.79129i	400.703			−423.193	+	288.186i		−	243.000i	531.659	+	33.2812i
19.20	5.65268	−	5.66103i	−11.0227	+	11.0227i	−0.0944246	−	63.9999i	29.4894	−	29.4894i	0.0919959	+	124.708i	461.206			−362.839	−	361.237i		−	243.000i	−0.246120	−	333.634i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.f	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	48.7.l.a	✓	48
4.b	odd	2	1		192.7.l.a		48
8.b	even	2	1		384.7.l.b		48
8.d	odd	2	1		384.7.l.a		48
16.e	even	4	1		192.7.l.a		48
16.e	even	4	1		384.7.l.a		48
16.f	odd	4	1	inner	48.7.l.a	✓	48
16.f	odd	4	1		384.7.l.b		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
48.7.l.a	✓	48	1.a	even	1	1	trivial
48.7.l.a	✓	48	16.f	odd	4	1	inner
192.7.l.a		48	4.b	odd	2	1
192.7.l.a		48	16.e	even	4	1
384.7.l.a		48	8.d	odd	2	1
384.7.l.a		48	16.e	even	4	1
384.7.l.b		48	8.b	even	2	1
384.7.l.b		48	16.f	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(48, [\chi])\).