Newform orbit 2916.2.e.e

• Label: 2916.2.e.e
• Level: $2916$
• Weight: $2$
• Character orbit: 2916.e
• Analytic conductor: $23.284$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2916.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.2843772294\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{13} + 24 q^{19} - 30 q^{25} - 6 q^{31} + 36 q^{37} - 24 q^{43} - 48 q^{49} + 36 q^{55} - 60 q^{61} - 42 q^{67} + 120 q^{73} - 12 q^{79} - 72 q^{85} + 96 q^{91} - 66 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
973.1		0			0			0		−2.02687	+	3.51063i		0		0.620414	+	1.07459i		0			0			0
973.2		0			0			0		−1.61255	+	2.79301i		0		1.89940	+	3.28986i		0			0			0
973.3		0			0			0		−1.49642	+	2.59187i		0		−2.00767	−	3.47739i		0			0			0
973.4		0			0			0		−1.16084	+	2.01063i		0		−1.56011	−	2.70218i		0			0			0
973.5		0			0			0		−0.746522	+	1.29301i		0		−1.13336	−	1.96303i		0			0			0
973.6		0			0			0		−0.630392	+	1.09187i		0		2.18132	+	3.77816i		0			0			0
973.7		0			0			0		0.630392	−	1.09187i		0		2.18132	+	3.77816i		0			0			0
973.8		0			0			0		0.746522	−	1.29301i		0		−1.13336	−	1.96303i		0			0			0
973.9		0			0			0		1.16084	−	2.01063i		0		−1.56011	−	2.70218i		0			0			0
973.10		0			0			0		1.49642	−	2.59187i		0		−2.00767	−	3.47739i		0			0			0
973.11		0			0			0		1.61255	−	2.79301i		0		1.89940	+	3.28986i		0			0			0
973.12		0			0			0		2.02687	−	3.51063i		0		0.620414	+	1.07459i		0			0			0
1945.1		0			0			0		−2.02687	−	3.51063i		0		0.620414	−	1.07459i		0			0			0
1945.2		0			0			0		−1.61255	−	2.79301i		0		1.89940	−	3.28986i		0			0			0
1945.3		0			0			0		−1.49642	−	2.59187i		0		−2.00767	+	3.47739i		0			0			0
1945.4		0			0			0		−1.16084	−	2.01063i		0		−1.56011	+	2.70218i		0			0			0
1945.5		0			0			0		−0.746522	−	1.29301i		0		−1.13336	+	1.96303i		0			0			0
1945.6		0			0			0		−0.630392	−	1.09187i		0		2.18132	−	3.77816i		0			0			0
1945.7		0			0			0		0.630392	+	1.09187i		0		2.18132	−	3.77816i		0			0			0
1945.8		0			0			0		0.746522	+	1.29301i		0		−1.13336	+	1.96303i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
9.c	even	3	1	inner
9.d	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2916.2.e.e		24
3.b	odd	2	1	inner	2916.2.e.e		24
9.c	even	3	1		2916.2.a.e	✓	12
9.c	even	3	1	inner	2916.2.e.e		24
9.d	odd	6	1		2916.2.a.e	✓	12
9.d	odd	6	1	inner	2916.2.e.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2916.2.a.e	✓	12	9.c	even	3	1
2916.2.a.e	✓	12	9.d	odd	6	1
2916.2.e.e		24	1.a	even	1	1	trivial
2916.2.e.e		24	3.b	odd	2	1	inner
2916.2.e.e		24	9.c	even	3	1	inner
2916.2.e.e		24	9.d	odd	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 45*T5^22 + 1260*T5^20 + 22023*T5^18 + 281475*T5^16 + 2565108*T5^14 + 17595873*T5^12 + 85978260*T5^10 + 310206267*T5^8 + 743964183*T5^6 + 1284013944*T5^4 + 1309792113*T5^2 + 855036081