Newform orbit 1900.2.l.d

• Label: 1900.2.l.d
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.l
• Analytic conductor: $15.172$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.1715763840\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{11} + 24 q^{61} + 24 q^{81}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
493.1		0		−2.05446	+	2.05446i		0			0			0		2.28491	−	2.28491i		0			−	5.44162i		0
493.2		0		−2.05446	+	2.05446i		0			0			0		−2.28491	+	2.28491i		0			−	5.44162i		0
493.3		0		−1.05614	+	1.05614i		0			0			0		−1.45445	+	1.45445i		0				0.769150i		0
493.4		0		−1.05614	+	1.05614i		0			0			0		1.45445	−	1.45445i		0				0.769150i		0
493.5		0		−0.814717	+	0.814717i		0			0			0		−1.28987	+	1.28987i		0				1.67247i		0
493.6		0		−0.814717	+	0.814717i		0			0			0		1.28987	−	1.28987i		0				1.67247i		0
493.7		0		0.814717	−	0.814717i		0			0			0		−1.28987	+	1.28987i		0				1.67247i		0
493.8		0		0.814717	−	0.814717i		0			0			0		1.28987	−	1.28987i		0				1.67247i		0
493.9		0		1.05614	−	1.05614i		0			0			0		−1.45445	+	1.45445i		0				0.769150i		0
493.10		0		1.05614	−	1.05614i		0			0			0		1.45445	−	1.45445i		0				0.769150i		0
493.11		0		2.05446	−	2.05446i		0			0			0		2.28491	−	2.28491i		0			−	5.44162i		0
493.12		0		2.05446	−	2.05446i		0			0			0		−2.28491	+	2.28491i		0			−	5.44162i		0
1557.1		0		−2.05446	−	2.05446i		0			0			0		2.28491	+	2.28491i		0				5.44162i		0
1557.2		0		−2.05446	−	2.05446i		0			0			0		−2.28491	−	2.28491i		0				5.44162i		0
1557.3		0		−1.05614	−	1.05614i		0			0			0		−1.45445	−	1.45445i		0			−	0.769150i		0
1557.4		0		−1.05614	−	1.05614i		0			0			0		1.45445	+	1.45445i		0			−	0.769150i		0
1557.5		0		−0.814717	−	0.814717i		0			0			0		−1.28987	−	1.28987i		0			−	1.67247i		0
1557.6		0		−0.814717	−	0.814717i		0			0			0		1.28987	+	1.28987i		0			−	1.67247i		0
1557.7		0		0.814717	+	0.814717i		0			0			0		−1.28987	−	1.28987i		0			−	1.67247i		0
1557.8		0		0.814717	+	0.814717i		0			0			0		1.28987	+	1.28987i		0			−	1.67247i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
5.c	odd	4	2	inner
19.b	odd	2	1	inner
95.d	odd	2	1	inner
95.g	even	4	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1900.2.l.d	✓	24
5.b	even	2	1	inner	1900.2.l.d	✓	24
5.c	odd	4	2	inner	1900.2.l.d	✓	24
19.b	odd	2	1	inner	1900.2.l.d	✓	24
95.d	odd	2	1	inner	1900.2.l.d	✓	24
95.g	even	4	2	inner	1900.2.l.d	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1900.2.l.d	✓	24	1.a	even	1	1	trivial
1900.2.l.d	✓	24	5.b	even	2	1	inner
1900.2.l.d	✓	24	5.c	odd	4	2	inner
1900.2.l.d	✓	24	19.b	odd	2	1	inner
1900.2.l.d	✓	24	95.d	odd	2	1	inner
1900.2.l.d	✓	24	95.g	even	4	2	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} + 78T_{3}^{8} + 489T_{3}^{4} + 625 \) acting on \(S_{2}^{\mathrm{new}}(1900, [\chi])\).