Newform orbit 2394.2.e.d

• Label: 2394.2.e.d
• Level: $2394$
• Weight: $2$
• Character orbit: 2394.e
• Analytic conductor: $19.116$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(19.1161862439\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} - 8 q^{7} + 24 q^{16} + 24 q^{25} + 8 q^{28} + 32 q^{43} - 24 q^{49} + 16 q^{58} - 24 q^{64} - 64 q^{85}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1063.1		−	1.00000i		0		−1.00000				−	0.575772i		0		−2.19869	+	1.47165i			1.00000i		0		−0.575772
1063.2		−	1.00000i		0		−1.00000					0.575772i		0		−2.19869	+	1.47165i			1.00000i		0		0.575772
1063.3			1.00000i		0		−1.00000					0.575772i		0		−2.19869	−	1.47165i		−	1.00000i		0		−0.575772
1063.4			1.00000i		0		−1.00000				−	0.575772i		0		−2.19869	−	1.47165i		−	1.00000i		0		0.575772
1063.5		−	1.00000i		0		−1.00000				−	1.63913i		0		1.91223	+	1.82849i			1.00000i		0		−1.63913
1063.6		−	1.00000i		0		−1.00000					1.63913i		0		1.91223	+	1.82849i			1.00000i		0		1.63913
1063.7			1.00000i		0		−1.00000					1.63913i		0		1.91223	−	1.82849i		−	1.00000i		0		−1.63913
1063.8			1.00000i		0		−1.00000				−	1.63913i		0		1.91223	−	1.82849i		−	1.00000i		0		1.63913
1063.9		−	1.00000i		0		−1.00000					2.99695i		0		−0.713538	−	2.54772i			1.00000i		0		2.99695
1063.10		−	1.00000i		0		−1.00000				−	2.99695i		0		−0.713538	−	2.54772i			1.00000i		0		−2.99695
1063.11			1.00000i		0		−1.00000				−	2.99695i		0		−0.713538	+	2.54772i		−	1.00000i		0		2.99695
1063.12			1.00000i		0		−1.00000					2.99695i		0		−0.713538	+	2.54772i		−	1.00000i		0		−2.99695
1063.13		−	1.00000i		0		−1.00000					1.63913i		0		1.91223	−	1.82849i			1.00000i		0		1.63913
1063.14		−	1.00000i		0		−1.00000				−	1.63913i		0		1.91223	−	1.82849i			1.00000i		0		−1.63913
1063.15			1.00000i		0		−1.00000				−	1.63913i		0		1.91223	+	1.82849i		−	1.00000i		0		1.63913
1063.16			1.00000i		0		−1.00000					1.63913i		0		1.91223	+	1.82849i		−	1.00000i		0		−1.63913
1063.17		−	1.00000i		0		−1.00000				−	2.99695i		0		−0.713538	+	2.54772i			1.00000i		0		−2.99695
1063.18		−	1.00000i		0		−1.00000					2.99695i		0		−0.713538	+	2.54772i			1.00000i		0		2.99695
1063.19			1.00000i		0		−1.00000					2.99695i		0		−0.713538	−	2.54772i		−	1.00000i		0		−2.99695
1063.20			1.00000i		0		−1.00000				−	2.99695i		0		−0.713538	−	2.54772i		−	1.00000i		0		2.99695

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.b	odd	2	1	inner
19.b	odd	2	1	inner
21.c	even	2	1	inner
57.d	even	2	1	inner
133.c	even	2	1	inner
399.h	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2394.2.e.d	✓	24
3.b	odd	2	1	inner	2394.2.e.d	✓	24
7.b	odd	2	1	inner	2394.2.e.d	✓	24
19.b	odd	2	1	inner	2394.2.e.d	✓	24
21.c	even	2	1	inner	2394.2.e.d	✓	24
57.d	even	2	1	inner	2394.2.e.d	✓	24
133.c	even	2	1	inner	2394.2.e.d	✓	24
399.h	odd	2	1	inner	2394.2.e.d	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2394.2.e.d	✓	24	1.a	even	1	1	trivial
2394.2.e.d	✓	24	3.b	odd	2	1	inner
2394.2.e.d	✓	24	7.b	odd	2	1	inner
2394.2.e.d	✓	24	19.b	odd	2	1	inner
2394.2.e.d	✓	24	21.c	even	2	1	inner
2394.2.e.d	✓	24	57.d	even	2	1	inner
2394.2.e.d	✓	24	133.c	even	2	1	inner
2394.2.e.d	✓	24	399.h	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2394, [\chi])\):

\( T_{5}^{6} + 12T_{5}^{4} + 28T_{5}^{2} + 8 \)

\( T_{13}^{6} - 44T_{13}^{4} + 140T_{13}^{2} - 72 \)