Newform orbit 930.2.e.a

• Label: 930.2.e.a
• Level: $930$
• Weight: $2$
• Character orbit: 930.e
• Analytic conductor: $7.426$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.42608738798\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
929.1	−1.00000			−1.70787	−	0.288390i	1.00000			2.10277	−	0.760496i	1.70787	+	0.288390i			4.63015i	−1.00000			2.83366	+	0.985067i	−2.10277	+	0.760496i
929.2	−1.00000			−1.70787	+	0.288390i	1.00000			2.10277	+	0.760496i	1.70787	−	0.288390i		−	4.63015i	−1.00000			2.83366	−	0.985067i	−2.10277	−	0.760496i
929.3	−1.00000			−1.69795	−	0.341995i	1.00000			−1.23971	−	1.86095i	1.69795	+	0.341995i			0.843688i	−1.00000			2.76608	+	1.16138i	1.23971	+	1.86095i
929.4	−1.00000			−1.69795	+	0.341995i	1.00000			−1.23971	+	1.86095i	1.69795	−	0.341995i		−	0.843688i	−1.00000			2.76608	−	1.16138i	1.23971	−	1.86095i
929.5	−1.00000			−1.63502	−	0.571593i	1.00000			1.46321	−	1.69086i	1.63502	+	0.571593i		−	2.83992i	−1.00000			2.34656	+	1.86913i	−1.46321	+	1.69086i
929.6	−1.00000			−1.63502	+	0.571593i	1.00000			1.46321	+	1.69086i	1.63502	−	0.571593i			2.83992i	−1.00000			2.34656	−	1.86913i	−1.46321	−	1.69086i
929.7	−1.00000			−1.36636	−	1.06445i	1.00000			−2.16820	+	0.546716i	1.36636	+	1.06445i		−	1.97405i	−1.00000			0.733873	+	2.90885i	2.16820	−	0.546716i
929.8	−1.00000			−1.36636	+	1.06445i	1.00000			−2.16820	−	0.546716i	1.36636	−	1.06445i			1.97405i	−1.00000			0.733873	−	2.90885i	2.16820	+	0.546716i
929.9	−1.00000			−1.02858	−	1.39357i	1.00000			0.467590	+	2.18663i	1.02858	+	1.39357i			1.43029i	−1.00000			−0.884063	+	2.86678i	−0.467590	−	2.18663i
929.10	−1.00000			−1.02858	+	1.39357i	1.00000			0.467590	−	2.18663i	1.02858	−	1.39357i		−	1.43029i	−1.00000			−0.884063	−	2.86678i	−0.467590	+	2.18663i
929.11	−1.00000			−0.880669	−	1.49145i	1.00000			2.09732	+	0.775395i	0.880669	+	1.49145i		−	0.657746i	−1.00000			−1.44884	+	2.62695i	−2.09732	−	0.775395i
929.12	−1.00000			−0.880669	+	1.49145i	1.00000			2.09732	−	0.775395i	0.880669	−	1.49145i			0.657746i	−1.00000			−1.44884	−	2.62695i	−2.09732	+	0.775395i
929.13	−1.00000			−0.522710	−	1.65129i	1.00000			−1.93647	+	1.11808i	0.522710	+	1.65129i			3.41776i	−1.00000			−2.45355	+	1.72630i	1.93647	−	1.11808i
929.14	−1.00000			−0.522710	+	1.65129i	1.00000			−1.93647	−	1.11808i	0.522710	−	1.65129i		−	3.41776i	−1.00000			−2.45355	−	1.72630i	1.93647	+	1.11808i
929.15	−1.00000			−0.230519	−	1.71664i	1.00000			−0.286520	−	2.21764i	0.230519	+	1.71664i			4.09004i	−1.00000			−2.89372	+	0.791438i	0.286520	+	2.21764i
929.16	−1.00000			−0.230519	+	1.71664i	1.00000			−0.286520	+	2.21764i	0.230519	−	1.71664i		−	4.09004i	−1.00000			−2.89372	−	0.791438i	0.286520	−	2.21764i
929.17	−1.00000			0.230519	−	1.71664i	1.00000			−0.286520	+	2.21764i	−0.230519	+	1.71664i		−	4.09004i	−1.00000			−2.89372	−	0.791438i	0.286520	−	2.21764i
929.18	−1.00000			0.230519	+	1.71664i	1.00000			−0.286520	−	2.21764i	−0.230519	−	1.71664i			4.09004i	−1.00000			−2.89372	+	0.791438i	0.286520	+	2.21764i
929.19	−1.00000			0.522710	−	1.65129i	1.00000			−1.93647	−	1.11808i	−0.522710	+	1.65129i		−	3.41776i	−1.00000			−2.45355	−	1.72630i	1.93647	+	1.11808i
929.20	−1.00000			0.522710	+	1.65129i	1.00000			−1.93647	+	1.11808i	−0.522710	−	1.65129i			3.41776i	−1.00000			−2.45355	+	1.72630i	1.93647	−	1.11808i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
15.d	odd	2	1	inner
31.b	odd	2	1	inner
465.g	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	930.2.e.a	✓	32
3.b	odd	2	1		930.2.e.b	yes	32
5.b	even	2	1		930.2.e.b	yes	32
15.d	odd	2	1	inner	930.2.e.a	✓	32
31.b	odd	2	1	inner	930.2.e.a	✓	32
93.c	even	2	1		930.2.e.b	yes	32
155.c	odd	2	1		930.2.e.b	yes	32
465.g	even	2	1	inner	930.2.e.a	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
930.2.e.a	✓	32	1.a	even	1	1	trivial
930.2.e.a	✓	32	15.d	odd	2	1	inner
930.2.e.a	✓	32	31.b	odd	2	1	inner
930.2.e.a	✓	32	465.g	even	2	1	inner
930.2.e.b	yes	32	3.b	odd	2	1
930.2.e.b	yes	32	5.b	even	2	1
930.2.e.b	yes	32	93.c	even	2	1
930.2.e.b	yes	32	155.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{47}^{8} + T_{47}^{7} - 234T_{47}^{6} - 252T_{47}^{5} + 15056T_{47}^{4} + 12776T_{47}^{3} - 268088T_{47}^{2} - 10752T_{47} + 55296 \) acting on \(S_{2}^{\mathrm{new}}(930, [\chi])\).