Newform orbit 48.5.i.a

• Label: 48.5.i.a
• Level: $48$
• Weight: $5$
• Character orbit: 48.i
• Analytic conductor: $4.962$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.96175822802\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(30\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 2 q^{3} - 4 q^{4} - 68 q^{6}+O(q^{10}) \)

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	−3.99998	+	0.0120968i	−4.29675	+	7.90809i	15.9997	−	0.0967736i	21.9903	−	21.9903i	17.0913	−	31.6842i			77.1285i	−63.9974	+	0.580637i	−44.0758	−	67.9582i	−87.6947	+	88.2267i
5.2	−3.98827	+	0.306169i	7.27370	−	5.30031i	15.8125	−	2.44216i	2.97955	−	2.97955i	−27.3866	+	23.3660i			5.93984i	−62.3168	+	14.5813i	24.8134	−	77.1058i	−10.9710	+	12.7955i
5.3	−3.84751	−	1.09391i	5.82159	+	6.86360i	13.6067	+	8.41770i	−20.5976	+	20.5976i	−14.8904	−	32.7761i		−	44.8073i	−43.1437	−	47.2718i	−13.2181	+	79.9142i	101.781	−	56.7174i
5.4	−3.69713	−	1.52683i	−8.89463	−	1.37314i	11.3376	+	11.2898i	−13.4157	+	13.4157i	30.7881	+	18.6573i		−	4.18833i	−24.6791	−	59.0503i	77.2290	+	24.4272i	70.0832	−	29.1162i
5.5	−3.47271	+	1.98501i	−4.74405	−	7.64814i	8.11943	−	13.7868i	−3.34416	+	3.34416i	31.6564	+	17.1428i			6.36882i	−0.829500	+	63.9946i	−35.9881	+	72.5662i	4.97509	−	18.2515i
5.6	−3.16452	−	2.44659i	−1.45703	−	8.88128i	4.02839	+	15.4846i	30.0724	−	30.0724i	−17.1180	+	31.6697i		−	37.1392i	25.1365	−	58.8571i	−76.7541	+	25.8807i	−168.740	+	21.5899i
5.7	−3.01530	+	2.62831i	−5.72284	+	6.94616i	2.18401	−	15.8502i	−22.2177	+	22.2177i	−1.00059	−	35.9861i		−	25.7845i	35.0739	+	53.5334i	−15.4983	−	79.5035i	8.59799	−	125.388i
5.8	−2.98404	+	2.66374i	6.71421	+	5.99328i	1.80902	−	15.8974i	27.3100	−	27.3100i	−36.0000		0.000682234i		−	70.5035i	36.9483	+	52.2573i	9.16120	+	80.4803i	−8.74755	+	154.241i
5.9	−2.23278	−	3.31884i	8.02371	+	4.07678i	−6.02942	+	14.8205i	12.9156	−	12.9156i	−4.38496	−	35.7319i			84.6751i	62.6491	−	13.0801i	47.7598	+	65.4217i	−71.7023	−	14.0272i
5.10	−2.12409	−	3.38943i	3.23855	−	8.39713i	−6.97648	+	14.3989i	−31.4183	+	31.4183i	−35.3405	+	6.85944i			26.1649i	63.6228	−	6.93833i	−60.0236	−	54.3890i	173.225	+	39.7548i
5.11	−2.02902	−	3.44718i	−3.29492	+	8.37517i	−7.76615	+	13.9888i	8.78364	−	8.78364i	35.5562	−	5.63519i		−	70.1022i	63.9797	−	1.61227i	−59.2870	−	55.1911i	−48.1010	−	12.4566i
5.12	−1.96807	+	3.48234i	8.97524	−	0.667113i	−8.25342	−	13.7070i	−17.7419	+	17.7419i	−15.3408	+	32.5678i			66.4694i	63.9757	−	1.76496i	80.1099	−	11.9750i	−26.8661	−	96.7008i
5.13	−1.13167	+	3.83658i	−8.98791	−	0.466380i	−13.4387	−	8.68346i	23.5639	−	23.5639i	11.9606	−	33.9550i			30.4899i	48.5229	−	41.7317i	80.5650	+	8.38356i	63.7382	+	117.071i
5.14	−0.431020	+	3.97671i	2.29223	−	8.70320i	−15.6284	−	3.42808i	−3.74626	+	3.74626i	33.6221	+	12.8668i		−	71.9695i	20.3687	−	60.6722i	−70.4914	−	39.8994i	−13.2831	−	16.5125i
5.15	−0.312407	−	3.98778i	−8.85016	−	1.63546i	−15.8048	+	2.49162i	2.85930	−	2.85930i	−3.75701	+	35.8034i			27.2580i	14.8736	+	62.2477i	75.6505	+	28.9482i	−12.2955	−	10.5090i
5.16	0.312407	+	3.98778i	1.63546	+	8.85016i	−15.8048	+	2.49162i	−2.85930	+	2.85930i	−34.7816	+	9.28671i			27.2580i	−14.8736	−	62.2477i	−75.6505	+	28.9482i	−12.2955	−	10.5090i
5.17	0.431020	−	3.97671i	8.70320	−	2.29223i	−15.6284	−	3.42808i	3.74626	−	3.74626i	−5.36427	−	35.5981i		−	71.9695i	−20.3687	+	60.6722i	70.4914	−	39.8994i	−13.2831	−	16.5125i
5.18	1.13167	−	3.83658i	0.466380	+	8.98791i	−13.4387	−	8.68346i	−23.5639	+	23.5639i	35.0106	+	8.38202i			30.4899i	−48.5229	+	41.7317i	−80.5650	+	8.38356i	63.7382	+	117.071i
5.19	1.96807	−	3.48234i	0.667113	−	8.97524i	−8.25342	−	13.7070i	17.7419	−	17.7419i	−29.9419	−	19.9870i			66.4694i	−63.9757	+	1.76496i	−80.1099	−	11.9750i	−26.8661	−	96.7008i
5.20	2.02902	+	3.44718i	−8.37517	+	3.29492i	−7.76615	+	13.9888i	−8.78364	+	8.78364i	−28.3516	−	22.1853i		−	70.1022i	−63.9797	+	1.61227i	59.2870	−	55.1911i	−48.1010	−	12.4566i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
16.e	even	4	1	inner
48.i	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	48.5.i.a	✓	60
3.b	odd	2	1	inner	48.5.i.a	✓	60
4.b	odd	2	1		192.5.i.a		60
12.b	even	2	1		192.5.i.a		60
16.e	even	4	1	inner	48.5.i.a	✓	60
16.f	odd	4	1		192.5.i.a		60
48.i	odd	4	1	inner	48.5.i.a	✓	60
48.k	even	4	1		192.5.i.a		60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
48.5.i.a	✓	60	1.a	even	1	1	trivial
48.5.i.a	✓	60	3.b	odd	2	1	inner
48.5.i.a	✓	60	16.e	even	4	1	inner
48.5.i.a	✓	60	48.i	odd	4	1	inner
192.5.i.a		60	4.b	odd	2	1
192.5.i.a		60	12.b	even	2	1
192.5.i.a		60	16.f	odd	4	1
192.5.i.a		60	48.k	even	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(48, [\chi])\).