Newform orbit 930.2.r.b

• Label: 930.2.r.b
• Level: $930$
• Weight: $2$
• Character orbit: 930.r
• Analytic conductor: $7.426$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.42608738798\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
119.1	1.00000			−1.72090	−	0.196245i	1.00000			−1.99884	−	1.00231i	−1.72090	−	0.196245i	1.33698	+	0.771903i	1.00000			2.92298	+	0.675436i	−1.99884	−	1.00231i
119.2	1.00000			−1.71980	+	0.205656i	1.00000			0.949262	+	2.02457i	−1.71980	+	0.205656i	−1.56394	−	0.902941i	1.00000			2.91541	−	0.707375i	0.949262	+	2.02457i
119.3	1.00000			−1.67835	−	0.427964i	1.00000			1.21982	−	1.87404i	−1.67835	−	0.427964i	3.99716	+	2.30776i	1.00000			2.63369	+	1.43654i	1.21982	−	1.87404i
119.4	1.00000			−1.57047	−	0.730502i	1.00000			2.16005	−	0.578104i	−1.57047	−	0.730502i	−0.447461	−	0.258342i	1.00000			1.93273	+	2.29446i	2.16005	−	0.578104i
119.5	1.00000			−1.54584	+	0.781271i	1.00000			2.22270	−	0.244106i	−1.54584	+	0.781271i	−2.13997	−	1.23551i	1.00000			1.77923	−	2.41544i	2.22270	−	0.244106i
119.6	1.00000			−1.41787	−	0.994813i	1.00000			−1.58068	+	1.58160i	−1.41787	−	0.994813i	0.447461	+	0.258342i	1.00000			1.02069	+	2.82103i	−1.58068	+	1.58160i
119.7	1.00000			−1.30243	+	1.14178i	1.00000			1.95677	+	1.08215i	−1.30243	+	1.14178i	4.20156	+	2.42577i	1.00000			0.392656	−	2.97419i	1.95677	+	1.08215i
119.8	1.00000			−1.20980	−	1.23951i	1.00000			−2.23288	+	0.119376i	−1.20980	−	1.23951i	−3.99716	−	2.30776i	1.00000			−0.0727630	+	2.99912i	−2.23288	+	0.119376i
119.9	1.00000			−1.12217	+	1.31937i	1.00000			−1.92892	+	1.13105i	−1.12217	+	1.31937i	−0.996061	−	0.575076i	1.00000			−0.481481	−	2.96111i	−1.92892	+	1.13105i
119.10	1.00000			−1.12093	+	1.32043i	1.00000			−2.03226	−	0.932700i	−1.12093	+	1.32043i	1.69016	+	0.975816i	1.00000			−0.487050	−	2.96020i	−2.03226	−	0.932700i
119.11	1.00000			−1.03040	−	1.39222i	1.00000			0.131393	−	2.23220i	−1.03040	−	1.39222i	−1.33698	−	0.771903i	1.00000			−0.876543	+	2.86909i	0.131393	−	2.23220i
119.12	1.00000			−0.882485	+	1.49038i	1.00000			1.20301	−	1.88488i	−0.882485	+	1.49038i	−3.11576	−	1.79889i	1.00000			−1.44244	−	2.63047i	1.20301	−	1.88488i
119.13	1.00000			−0.681795	−	1.59222i	1.00000			1.27870	+	1.83437i	−0.681795	−	1.59222i	1.56394	+	0.902941i	1.00000			−2.07031	+	2.17113i	1.27870	+	1.83437i
119.14	1.00000			−0.392310	+	1.68704i	1.00000			0.381329	+	2.20331i	−0.392310	+	1.68704i	−2.96938	−	1.71437i	1.00000			−2.69219	−	1.32368i	0.381329	+	2.20331i
119.15	1.00000			−0.0963182	−	1.72937i	1.00000			−1.32275	+	1.80286i	−0.0963182	−	1.72937i	2.13997	+	1.23551i	1.00000			−2.98145	+	0.333140i	−1.32275	+	1.80286i
119.16	1.00000			0.180653	+	1.72260i	1.00000			0.550525	−	2.16724i	0.180653	+	1.72260i	2.86191	+	1.65233i	1.00000			−2.93473	+	0.622388i	0.550525	−	2.16724i
119.17	1.00000			0.256671	+	1.71293i	1.00000			−1.42705	−	1.72149i	0.256671	+	1.71293i	−2.76619	−	1.59706i	1.00000			−2.86824	+	0.879317i	−1.42705	−	1.72149i
119.18	1.00000			0.337599	−	1.69883i	1.00000			−0.0412189	+	2.23569i	0.337599	−	1.69883i	−4.20156	−	2.42577i	1.00000			−2.77205	−	1.14705i	−0.0412189	+	2.23569i
119.19	1.00000			0.442238	+	1.67464i	1.00000			−1.20088	+	1.88624i	0.442238	+	1.67464i	2.75588	+	1.59111i	1.00000			−2.60885	+	1.48118i	−1.20088	+	1.88624i
119.20	1.00000			0.552753	+	1.64148i	1.00000			2.23391	+	0.0983151i	0.552753	+	1.64148i	1.38670	+	0.800613i	1.00000			−2.38893	+	1.81467i	2.23391	+	0.0983151i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
15.d	odd	2	1	inner
31.e	odd	6	1	inner
465.t	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	930.2.r.b	yes	64
3.b	odd	2	1		930.2.r.a	✓	64
5.b	even	2	1		930.2.r.a	✓	64
15.d	odd	2	1	inner	930.2.r.b	yes	64
31.e	odd	6	1	inner	930.2.r.b	yes	64
93.g	even	6	1		930.2.r.a	✓	64
155.i	odd	6	1		930.2.r.a	✓	64
465.t	even	6	1	inner	930.2.r.b	yes	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
930.2.r.a	✓	64	3.b	odd	2	1
930.2.r.a	✓	64	5.b	even	2	1
930.2.r.a	✓	64	93.g	even	6	1
930.2.r.a	✓	64	155.i	odd	6	1
930.2.r.b	yes	64	1.a	even	1	1	trivial
930.2.r.b	yes	64	15.d	odd	2	1	inner
930.2.r.b	yes	64	31.e	odd	6	1	inner
930.2.r.b	yes	64	465.t	even	6	1	inner