Newform orbit 763.2.u.a

• Label: 763.2.u.a
• Level: $763$
• Weight: $2$
• Character orbit: 763.u
• Analytic conductor: $6.093$
• Analytic rank: $0$
• Dimension: $144$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 763 = 7 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	763.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.09258567422\)
Analytic rank:	\(0\)
Dimension:	\(144\)
Relative dimension:	\(72\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 144 q - 3 q^{2} + 2 q^{3} + 69 q^{4} - 3 q^{5} - 6 q^{6} - 3 q^{7} + 146 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
46.1	−2.44207	+	1.40993i	−2.77727			2.97579	−	5.15422i	0.578779	−	1.00247i	6.78228	−	3.91575i	2.46112	+	0.971015i			11.1429i	4.71324					3.26414i
46.2	−2.34404	+	1.35333i	2.18668			2.66301	−	4.61247i	−0.657496	+	1.13882i	−5.12565	+	2.95930i	0.749983	−	2.53723i			9.00242i	1.78155				−	3.55924i
46.3	−2.32352	+	1.34148i	−0.624963			2.59916	−	4.50187i	0.901408	−	1.56128i	1.45211	−	0.838378i	−2.63801	+	0.202239i			8.58098i	−2.60942					4.83690i
46.4	−2.28118	+	1.31704i	3.28730			2.46919	−	4.27677i	1.51609	−	2.62595i	−7.49893	+	4.32951i	−1.49954	+	2.17976i			7.73995i	7.80636					7.98703i
46.5	−2.19298	+	1.26612i	−0.450206			2.20611	−	3.82109i	−1.60397	+	2.77816i	0.987293	−	0.570014i	−1.26216	−	2.32529i			6.10830i	−2.79731				−	8.12326i
46.6	−2.10435	+	1.21495i	1.34093			1.95221	−	3.38132i	0.526421	−	0.911788i	−2.82179	+	1.62916i	2.26964	+	1.35968i			4.62753i	−1.20191					2.55830i
46.7	−2.04106	+	1.17841i	−2.92744			1.77730	−	3.07837i	−0.755619	+	1.30877i	5.97509	−	3.44972i	−0.817484	−	2.51629i			3.66389i	5.56991				−	3.56171i
46.8	−2.04075	+	1.17823i	−0.163771			1.77645	−	3.07690i	1.61531	−	2.79781i	0.334215	−	0.192959i	1.73108	−	2.00084i			3.65935i	−2.97318					7.61284i
46.9	−1.93843	+	1.11915i	2.66036			1.50501	−	2.60675i	−1.84656	+	3.19833i	−5.15692	+	2.97735i	−2.43969	+	1.02367i			2.26073i	4.07750				−	8.26632i
46.10	−1.91163	+	1.10368i	−1.42639			1.43622	−	2.48761i	−1.14869	+	1.98959i	2.72674	−	1.57428i	2.62087	+	0.362004i			1.92580i	−0.965400				−	5.07116i
46.11	−1.87656	+	1.08344i	−2.37192			1.34766	−	2.33422i	−0.348935	+	0.604372i	4.45105	−	2.56982i	−0.906983	+	2.48543i			1.50669i	2.62599				−	1.51219i
46.12	−1.79409	+	1.03582i	2.05489			1.14584	−	1.98465i	−1.40120	+	2.42695i	−3.68667	+	2.12850i	2.06400	+	1.65527i			0.604254i	1.22259				−	5.80555i
46.13	−1.76164	+	1.01708i	−2.25166			1.06891	−	1.85141i	1.98798	−	3.44329i	3.96661	−	2.29012i	−2.46116	+	0.970924i			0.280363i	2.06997					8.08777i
46.14	−1.66285	+	0.960049i	0.592603			0.843389	−	1.46079i	−0.242731	+	0.420422i	−0.985413	+	0.568928i	−2.63024	−	0.286094i		−	0.601416i	−2.64882				−	0.932135i
46.15	−1.56716	+	0.904800i	1.78899			0.637326	−	1.10388i	1.59166	−	2.75684i	−2.80364	+	1.61868i	−2.02609	−	1.70146i		−	1.31259i	0.200503					5.76054i
46.16	−1.46930	+	0.848298i	−1.05990			0.439220	−	0.760751i	0.822697	−	1.42495i	1.55731	−	0.899113i	0.776079	+	2.52937i		−	1.90284i	−1.87661					2.79157i
46.17	−1.45769	+	0.841596i	−0.944127			0.416568	−	0.721517i	0.323854	−	0.560932i	1.37624	−	0.794573i	1.24117	−	2.33656i		−	1.96406i	−2.10862					1.09022i
46.18	−1.42205	+	0.821020i	3.32048			0.348147	−	0.603008i	−0.591205	+	1.02400i	−4.72188	+	2.72618i	1.59160	−	2.11348i		−	2.14074i	8.02556				−	1.94156i
46.19	−1.35494	+	0.782277i	0.813163			0.223916	−	0.387834i	−1.17665	+	2.03801i	−1.10179	+	0.636119i	2.12033	−	1.58246i		−	2.42845i	−2.33877				−	3.68186i
46.20	−1.29993	+	0.750517i	−3.24919			0.126550	−	0.219191i	1.92722	−	3.33804i	4.22373	−	2.43857i	2.55238	−	0.696666i		−	2.62215i	7.55722					5.78563i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
763.u	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	763.2.u.a	yes	144
7.c	even	3	1		763.2.r.a	✓	144
109.e	even	6	1		763.2.r.a	✓	144
763.u	even	6	1	inner	763.2.u.a	yes	144

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
763.2.r.a	✓	144	7.c	even	3	1
763.2.r.a	✓	144	109.e	even	6	1
763.2.u.a	yes	144	1.a	even	1	1	trivial
763.2.u.a	yes	144	763.u	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(763, [\chi])\).