Newform orbit 104.3.n.b

• Label: 104.3.n.b
• Level: $104$
• Weight: $3$
• Character orbit: 104.n
• Analytic conductor: $2.834$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	104.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.83379474935\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(24\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 5 q^{2} + 6 q^{3} + 7 q^{4} - 6 q^{6} + 46 q^{8} - 54 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.99943	+	0.0477012i	1.29933	+	2.25050i	3.99545	−	0.190750i			6.92815i	−2.70526	−	4.43773i	−3.63730	−	2.10000i	−7.97953	+	0.571980i	1.12351	−	1.94597i	−0.330481	−	13.8524i
3.2	−1.94740	−	0.455687i	−0.811605	−	1.40574i	3.58470	+	1.77481i			0.300018i	0.939938	+	3.10737i	5.76473	+	3.32827i	−6.17207	−	5.08975i	3.18259	−	5.51241i	0.136715	−	0.584255i
3.3	−1.85966	+	0.735988i	1.03791	+	1.79771i	2.91664	−	2.73737i		−	7.15267i	−3.25325	−	2.57924i	−6.75868	−	3.90213i	−3.40928	+	7.23718i	2.34549	−	4.06250i	5.26428	+	13.3015i
3.4	−1.84763	+	0.765678i	−2.49899	−	4.32838i	2.82747	−	2.82938i		−	2.20232i	7.93136	+	6.08382i	−1.56924	−	0.906000i	−3.05773	+	7.39258i	−7.98992	+	13.8389i	1.68627	+	4.06908i
3.5	−1.71322	−	1.03192i	2.54318	+	4.40492i	1.87027	+	3.53583i		−	5.96349i	0.188492	−	10.1710i	5.66618	+	3.27137i	0.444497	−	7.98764i	−8.43552	+	14.6108i	−6.15386	+	10.2168i
3.6	−1.42220	−	1.40618i	−2.42654	−	4.20288i	0.0453004	+	3.99974i			8.44950i	−2.45900	+	9.38949i	−5.72012	−	3.30251i	5.55994	−	5.75213i	−7.27615	+	12.6027i	11.8815	−	12.0169i
3.7	−1.34706	+	1.47832i	−0.665721	−	1.15306i	−0.370871	−	3.98277i			2.40360i	2.60136	+	0.569092i	2.97615	+	1.71828i	6.38740	+	4.81675i	3.61363	−	6.25899i	−3.55329	−	3.23779i
3.8	−1.33890	+	1.48571i	2.62138	+	4.54036i	−0.414681	−	3.97845i			2.07640i	−10.2554	−	2.18449i	7.93561	+	4.58163i	6.46604	+	4.71066i	−9.24327	+	16.0098i	−3.08493	−	2.78009i
3.9	−1.22511	−	1.58086i	0.395729	+	0.685423i	−0.998230	+	3.87344i		−	2.87446i	0.598747	−	1.46531i	−9.47495	−	5.47037i	7.34630	−	3.16731i	4.18680	−	7.25174i	−4.54411	+	3.52152i
3.10	−0.756511	−	1.85140i	0.395729	+	0.685423i	−2.85538	+	2.80121i			2.87446i	0.969621	−	1.25118i	9.47495	+	5.47037i	7.34630	+	3.16731i	4.18680	−	7.25174i	5.32178	−	2.17456i
3.11	−0.506690	−	1.93475i	−2.42654	−	4.20288i	−3.48653	+	1.96064i		−	8.44950i	−6.90203	+	6.82430i	5.72012	+	3.30251i	5.55994	+	5.75213i	−7.27615	+	12.6027i	−16.3477	+	4.28128i
3.12	−0.442087	+	1.95053i	−0.114985	−	0.199159i	−3.60912	−	1.72460i		−	8.95777i	0.439299	−	0.136235i	5.87230	+	3.39037i	4.95943	−	6.27726i	4.47356	−	7.74843i	17.4724	+	3.96011i
3.13	−0.439744	+	1.95106i	−1.39468	−	2.41566i	−3.61325	−	1.71593i			4.40424i	5.32640	−	1.65883i	−6.81539	−	3.93487i	4.93679	−	6.29509i	0.609719	−	1.05606i	−8.59292	−	1.93674i
3.14	−0.0370584	−	1.99966i	2.54318	+	4.40492i	−3.99725	+	0.148208i			5.96349i	8.71407	−	5.24872i	−5.66618	−	3.27137i	0.444497	+	7.98764i	−8.43552	+	14.6108i	11.9249	−	0.220997i
3.15	0.345572	+	1.96992i	1.51500	+	2.62405i	−3.76116	+	1.36150i			3.15472i	−4.64563	+	3.89122i	−0.883630	−	0.510164i	−3.98180	−	6.93868i	−0.0904296	+	0.156629i	−6.21454	+	1.09018i
3.16	0.579061	−	1.91434i	−0.811605	−	1.40574i	−3.32938	−	2.21704i		−	0.300018i	−3.16103	+	0.739677i	−5.76473	−	3.32827i	−6.17207	+	5.08975i	3.18259	−	5.51241i	−0.574337	−	0.173729i
3.17	1.04103	−	1.70771i	1.29933	+	2.25050i	−1.83253	−	3.55554i		−	6.92815i	5.19582	+	0.123959i	3.63730	+	2.10000i	−7.97953	−	0.571980i	1.12351	−	1.94597i	−11.8313	−	7.21239i
3.18	1.53321	+	1.28423i	1.51500	+	2.62405i	0.701487	+	3.93801i		−	3.15472i	−1.04708	+	5.96884i	0.883630	+	0.510164i	−3.98180	+	6.93868i	−0.0904296	+	0.156629i	4.05140	−	4.83686i
3.19	1.56721	−	1.24252i	1.03791	+	1.79771i	0.912310	−	3.89457i			7.15267i	3.86031	+	1.52778i	6.75868	+	3.90213i	−3.40928	−	7.23718i	2.34549	−	4.06250i	8.88730	+	11.2097i
3.20	1.58691	−	1.21726i	−2.49899	−	4.32838i	1.03658	−	3.86335i			2.20232i	−9.23442	−	3.82685i	1.56924	+	0.906000i	−3.05773	−	7.39258i	−7.98992	+	13.8389i	2.68079	+	3.49489i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
8.d	odd	2	1	inner
13.c	even	3	1	inner
104.n	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	104.3.n.b	✓	48
4.b	odd	2	1		416.3.v.b		48
8.b	even	2	1		416.3.v.b		48
8.d	odd	2	1	inner	104.3.n.b	✓	48
13.c	even	3	1	inner	104.3.n.b	✓	48
52.j	odd	6	1		416.3.v.b		48
104.n	odd	6	1	inner	104.3.n.b	✓	48
104.r	even	6	1		416.3.v.b		48

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
104.3.n.b	✓	48	1.a	even	1	1	trivial
104.3.n.b	✓	48	8.d	odd	2	1	inner
104.3.n.b	✓	48	13.c	even	3	1	inner
104.3.n.b	✓	48	104.n	odd	6	1	inner
416.3.v.b		48	4.b	odd	2	1
416.3.v.b		48	8.b	even	2	1
416.3.v.b		48	52.j	odd	6	1
416.3.v.b		48	104.r	even	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^24 - 3*T3^23 + 72*T3^22 - 165*T3^21 + 3165*T3^20 - 6590*T3^19 + 83013*T3^18 - 140189*T3^17 + 1509945*T3^16 - 2256630*T3^15 + 17339509*T3^14 - 18252565*T3^13 + 132212136*T3^12 - 105457131*T3^11 + 672823921*T3^10 - 231149460*T3^9 + 2112097828*T3^8 - 273954724*T3^7 + 4689947644*T3^6 + 450026384*T3^5 + 4981652496*T3^4 - 732989040*T3^3 + 2383109200*T3^2 + 488824000*T3 + 134560000