Newform orbit 936.2.dr.b

• Label: 936.2.dr.b
• Level: $936$
• Weight: $2$
• Character orbit: 936.dr
• Analytic conductor: $7.474$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dr (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.47399762919\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(8\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 4 q^{7} - 20 q^{13} - 4 q^{19} + 4 q^{31} + 60 q^{43} + 84 q^{49} - 28 q^{61} - 24 q^{67} + 16 q^{73} + 48 q^{79} + 88 q^{85} - 116 q^{91} + 72 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1		0			0			0		−2.43408	+	2.43408i		0		−0.0623138	−	0.232558i		0			0			0
89.2		0			0			0		−1.84163	+	1.84163i		0		−0.618766	−	2.30927i		0			0			0
89.3		0			0			0		−1.79153	+	1.79153i		0		1.02710	+	3.83317i		0			0			0
89.4		0			0			0		−0.491974	+	0.491974i		0		0.153985	+	0.574679i		0			0			0
89.5		0			0			0		0.491974	−	0.491974i		0		0.153985	+	0.574679i		0			0			0
89.6		0			0			0		1.79153	−	1.79153i		0		1.02710	+	3.83317i		0			0			0
89.7		0			0			0		1.84163	−	1.84163i		0		−0.618766	−	2.30927i		0			0			0
89.8		0			0			0		2.43408	−	2.43408i		0		−0.0623138	−	0.232558i		0			0			0
305.1		0			0			0		−2.43408	−	2.43408i		0		−0.0623138	+	0.232558i		0			0			0
305.2		0			0			0		−1.84163	−	1.84163i		0		−0.618766	+	2.30927i		0			0			0
305.3		0			0			0		−1.79153	−	1.79153i		0		1.02710	−	3.83317i		0			0			0
305.4		0			0			0		−0.491974	−	0.491974i		0		0.153985	−	0.574679i		0			0			0
305.5		0			0			0		0.491974	+	0.491974i		0		0.153985	−	0.574679i		0			0			0
305.6		0			0			0		1.79153	+	1.79153i		0		1.02710	−	3.83317i		0			0			0
305.7		0			0			0		1.84163	+	1.84163i		0		−0.618766	+	2.30927i		0			0			0
305.8		0			0			0		2.43408	+	2.43408i		0		−0.0623138	+	0.232558i		0			0			0
449.1		0			0			0		−2.65632	+	2.65632i		0		1.47941	+	0.396406i		0			0			0
449.2		0			0			0		−2.57811	+	2.57811i		0		−3.04951	−	0.817113i		0			0			0
449.3		0			0			0		−1.44645	+	1.44645i		0		4.86936	+	1.30474i		0			0			0
449.4		0			0			0		−0.661135	+	0.661135i		0		−2.79926	−	0.750059i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
13.f	odd	12	1	inner
39.k	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	936.2.dr.b	✓	32
3.b	odd	2	1	inner	936.2.dr.b	✓	32
13.f	odd	12	1	inner	936.2.dr.b	✓	32
39.k	even	12	1	inner	936.2.dr.b	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
936.2.dr.b	✓	32	1.a	even	1	1	trivial
936.2.dr.b	✓	32	3.b	odd	2	1	inner
936.2.dr.b	✓	32	13.f	odd	12	1	inner
936.2.dr.b	✓	32	39.k	even	12	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^32 + 622*T5^28 + 146079*T5^24 + 16099804*T5^20 + 851715007*T5^16 + 20672514558*T5^12 + 183996818865*T5^8 + 167355742680*T5^4 + 29376588816