Newform orbit 1900.3.g.d

• Label: 1900.3.g.d
• Level: $1900$
• Weight: $3$
• Character orbit: 1900.g
• Analytic conductor: $51.771$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1900.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(51.7712502285\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 104 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
949.1		0		−5.26531				0			0			0				12.1735i		0		18.7235				0
949.2		0		−5.26531				0			0			0			−	12.1735i		0		18.7235				0
949.3		0		−4.84257				0			0			0			−	6.85668i		0		14.4504				0
949.4		0		−4.84257				0			0			0				6.85668i		0		14.4504				0
949.5		0		−4.58743				0			0			0				1.52935i		0		12.0445				0
949.6		0		−4.58743				0			0			0			−	1.52935i		0		12.0445				0
949.7		0		−2.93221				0			0			0			−	5.62705i		0		−0.402160				0
949.8		0		−2.93221				0			0			0				5.62705i		0		−0.402160				0
949.9		0		−2.16913				0			0			0				8.18099i		0		−4.29489				0
949.10		0		−2.16913				0			0			0			−	8.18099i		0		−4.29489				0
949.11		0		−1.84332				0			0			0				10.5375i		0		−5.60216				0
949.12		0		−1.84332				0			0			0			−	10.5375i		0		−5.60216				0
949.13		0		−0.284180				0			0			0				2.19606i		0		−8.91924				0
949.14		0		−0.284180				0			0			0			−	2.19606i		0		−8.91924				0
949.15		0		0.284180				0			0			0				2.19606i		0		−8.91924				0
949.16		0		0.284180				0			0			0			−	2.19606i		0		−8.91924				0
949.17		0		1.84332				0			0			0				10.5375i		0		−5.60216				0
949.18		0		1.84332				0			0			0			−	10.5375i		0		−5.60216				0
949.19		0		2.16913				0			0			0				8.18099i		0		−4.29489				0
949.20		0		2.16913				0			0			0			−	8.18099i		0		−4.29489				0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1900.3.g.d		28
5.b	even	2	1	inner	1900.3.g.d		28
5.c	odd	4	1		1900.3.e.g	✓	14
5.c	odd	4	1		1900.3.e.h	yes	14
19.b	odd	2	1	inner	1900.3.g.d		28
95.d	odd	2	1	inner	1900.3.g.d		28
95.g	even	4	1		1900.3.e.g	✓	14
95.g	even	4	1		1900.3.e.h	yes	14

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1900.3.e.g	✓	14	5.c	odd	4	1
1900.3.e.g	✓	14	95.g	even	4	1
1900.3.e.h	yes	14	5.c	odd	4	1
1900.3.e.h	yes	14	95.g	even	4	1
1900.3.g.d		28	1.a	even	1	1	trivial
1900.3.g.d		28	5.b	even	2	1	inner
1900.3.g.d		28	19.b	odd	2	1	inner
1900.3.g.d		28	95.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} - 89T_{3}^{12} + 3026T_{3}^{10} - 49092T_{3}^{8} + 390297T_{3}^{6} - 1440495T_{3}^{4} + 1994425T_{3}^{2} - 151875 \) acting on \(S_{3}^{\mathrm{new}}(1900, [\chi])\).