Newform orbit 1904.2.j.b

• Label: 1904.2.j.b
• Level: $1904$
• Weight: $2$
• Character orbit: 1904.j
• Analytic conductor: $15.204$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1904.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.2035165449\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 32 q^{9} - 32 q^{25} - 8 q^{29} + 8 q^{49} + 40 q^{53} + 8 q^{57} - 48 q^{65} - 16 q^{77} + 24 q^{81} + 32 q^{93}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
783.1		0		−3.03955				0				3.73768i		0		2.48011	−	0.921434i		0		6.23886				0
783.2		0		−3.03955				0			−	3.73768i		0		2.48011	+	0.921434i		0		6.23886				0
783.3		0		−2.69181				0				1.35274i		0		−1.38205	+	2.25609i		0		4.24582				0
783.4		0		−2.69181				0			−	1.35274i		0		−1.38205	−	2.25609i		0		4.24582				0
783.5		0		−2.58390				0			−	2.47104i		0		−2.13370	+	1.56439i		0		3.67656				0
783.6		0		−2.58390				0				2.47104i		0		−2.13370	−	1.56439i		0		3.67656				0
783.7		0		−1.30773				0				0.506686i		0		2.04991	+	1.67268i		0		−1.28984				0
783.8		0		−1.30773				0			−	0.506686i		0		2.04991	−	1.67268i		0		−1.28984				0
783.9		0		−0.779152				0				1.55185i		0		0.732964	+	2.54220i		0		−2.39292				0
783.10		0		−0.779152				0			−	1.55185i		0		0.732964	−	2.54220i		0		−2.39292				0
783.11		0		−0.722167				0				3.66454i		0		−2.15567	+	1.53397i		0		−2.47847				0
783.12		0		−0.722167				0			−	3.66454i		0		−2.15567	−	1.53397i		0		−2.47847				0
783.13		0		0.722167				0				3.66454i		0		2.15567	−	1.53397i		0		−2.47847				0
783.14		0		0.722167				0			−	3.66454i		0		2.15567	+	1.53397i		0		−2.47847				0
783.15		0		0.779152				0				1.55185i		0		−0.732964	−	2.54220i		0		−2.39292				0
783.16		0		0.779152				0			−	1.55185i		0		−0.732964	+	2.54220i		0		−2.39292				0
783.17		0		1.30773				0				0.506686i		0		−2.04991	−	1.67268i		0		−1.28984				0
783.18		0		1.30773				0			−	0.506686i		0		−2.04991	+	1.67268i		0		−1.28984				0
783.19		0		2.58390				0			−	2.47104i		0		2.13370	−	1.56439i		0		3.67656				0
783.20		0		2.58390				0				2.47104i		0		2.13370	+	1.56439i		0		3.67656				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
7.b	odd	2	1	inner
28.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1904.2.j.b	✓	24
4.b	odd	2	1	inner	1904.2.j.b	✓	24
7.b	odd	2	1	inner	1904.2.j.b	✓	24
28.d	even	2	1	inner	1904.2.j.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1904.2.j.b	✓	24	1.a	even	1	1	trivial
1904.2.j.b	✓	24	4.b	odd	2	1	inner
1904.2.j.b	✓	24	7.b	odd	2	1	inner
1904.2.j.b	✓	24	28.d	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 26T_{3}^{10} + 245T_{3}^{8} - 1002T_{3}^{6} + 1679T_{3}^{4} - 1100T_{3}^{2} + 242 \) acting on \(S_{2}^{\mathrm{new}}(1904, [\chi])\).