Newform orbit 1900.2.s.e

• Label: 1900.2.s.e
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.s
• Analytic conductor: $15.172$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.1715763840\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
49.1		0		−2.74265	−	1.58347i		0			0			0				3.03607i		0		3.51475	+	6.08773i		0
49.2		0		−1.61567	−	0.932807i		0			0			0			−	3.93019i		0		0.240257	+	0.416137i		0
49.3		0		−1.59908	−	0.923228i		0			0			0				1.72830i		0		0.204702	+	0.354554i		0
49.4		0		−1.36682	−	0.789132i		0			0			0			−	1.39989i		0		−0.254541	−	0.440878i		0
49.5		0		−1.08524	−	0.626563i		0			0			0			−	2.18534i		0		−0.714838	−	1.23814i		0
49.6		0		−0.120414	−	0.0695210i		0			0			0				3.40785i		0		−1.49033	−	2.58133i		0
49.7		0		0.120414	+	0.0695210i		0			0			0			−	3.40785i		0		−1.49033	−	2.58133i		0
49.8		0		1.08524	+	0.626563i		0			0			0				2.18534i		0		−0.714838	−	1.23814i		0
49.9		0		1.36682	+	0.789132i		0			0			0				1.39989i		0		−0.254541	−	0.440878i		0
49.10		0		1.59908	+	0.923228i		0			0			0			−	1.72830i		0		0.204702	+	0.354554i		0
49.11		0		1.61567	+	0.932807i		0			0			0				3.93019i		0		0.240257	+	0.416137i		0
49.12		0		2.74265	+	1.58347i		0			0			0			−	3.03607i		0		3.51475	+	6.08773i		0
349.1		0		−2.74265	+	1.58347i		0			0			0			−	3.03607i		0		3.51475	−	6.08773i		0
349.2		0		−1.61567	+	0.932807i		0			0			0				3.93019i		0		0.240257	−	0.416137i		0
349.3		0		−1.59908	+	0.923228i		0			0			0			−	1.72830i		0		0.204702	−	0.354554i		0
349.4		0		−1.36682	+	0.789132i		0			0			0				1.39989i		0		−0.254541	+	0.440878i		0
349.5		0		−1.08524	+	0.626563i		0			0			0				2.18534i		0		−0.714838	+	1.23814i		0
349.6		0		−0.120414	+	0.0695210i		0			0			0			−	3.40785i		0		−1.49033	+	2.58133i		0
349.7		0		0.120414	−	0.0695210i		0			0			0				3.40785i		0		−1.49033	+	2.58133i		0
349.8		0		1.08524	−	0.626563i		0			0			0			−	2.18534i		0		−0.714838	+	1.23814i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.c	even	3	1	inner
95.i	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1900.2.s.e		24
5.b	even	2	1	inner	1900.2.s.e		24
5.c	odd	4	1		1900.2.i.e	✓	12
5.c	odd	4	1		1900.2.i.f	yes	12
19.c	even	3	1	inner	1900.2.s.e		24
95.i	even	6	1	inner	1900.2.s.e		24
95.m	odd	12	1		1900.2.i.e	✓	12
95.m	odd	12	1		1900.2.i.f	yes	12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1900.2.i.e	✓	12	5.c	odd	4	1
1900.2.i.e	✓	12	95.m	odd	12	1
1900.2.i.f	yes	12	5.c	odd	4	1
1900.2.i.f	yes	12	95.m	odd	12	1
1900.2.s.e		24	1.a	even	1	1	trivial
1900.2.s.e		24	5.b	even	2	1	inner
1900.2.s.e		24	19.c	even	3	1	inner
1900.2.s.e		24	95.i	even	6	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^24 - 21*T3^22 + 287*T3^20 - 2200*T3^18 + 12049*T3^16 - 46079*T3^14 + 132466*T3^12 - 270811*T3^10 + 406037*T3^8 - 380304*T3^6 + 224071*T3^4 - 4329*T3^2 + 81