Newform orbit 2900.2.s.e

• Label: 2900.2.s.e
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.s
• Analytic conductor: $23.157$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.s (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(23.1566165862\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 24 q^{9} + 8 q^{11} - 4 q^{19} + 20 q^{21} + 20 q^{29} + 8 q^{31} - 12 q^{39} - 12 q^{41} + 24 q^{61} + 56 q^{69} + 32 q^{79} - 24 q^{81} + 40 q^{89} - 52 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
157.1		0		−2.96392				0			0			0		−1.82634	−	1.82634i		0		5.78485				0
157.2		0		−2.88658				0			0			0		−1.88895	−	1.88895i		0		5.33237				0
157.3		0		−2.48528				0			0			0		0.680727	+	0.680727i		0		3.17662				0
157.4		0		−2.05310				0			0			0		1.91654	+	1.91654i		0		1.21523				0
157.5		0		−2.01141				0			0			0		1.64568	+	1.64568i		0		1.04576				0
157.6		0		−1.66623				0			0			0		0.406129	+	0.406129i		0		−0.223678				0
157.7		0		−1.04258				0			0			0		−3.54494	−	3.54494i		0		−1.91304				0
157.8		0		−0.673148				0			0			0		−1.34934	−	1.34934i		0		−2.54687				0
157.9		0		−0.357806				0			0			0		2.37536	+	2.37536i		0		−2.87197				0
157.10		0		−0.0272183				0			0			0		0.238631	+	0.238631i		0		−2.99926				0
157.11		0		0.0272183				0			0			0		−0.238631	−	0.238631i		0		−2.99926				0
157.12		0		0.357806				0			0			0		−2.37536	−	2.37536i		0		−2.87197				0
157.13		0		0.673148				0			0			0		1.34934	+	1.34934i		0		−2.54687				0
157.14		0		1.04258				0			0			0		3.54494	+	3.54494i		0		−1.91304				0
157.15		0		1.66623				0			0			0		−0.406129	−	0.406129i		0		−0.223678				0
157.16		0		2.01141				0			0			0		−1.64568	−	1.64568i		0		1.04576				0
157.17		0		2.05310				0			0			0		−1.91654	−	1.91654i		0		1.21523				0
157.18		0		2.48528				0			0			0		−0.680727	−	0.680727i		0		3.17662				0
157.19		0		2.88658				0			0			0		1.88895	+	1.88895i		0		5.33237				0
157.20		0		2.96392				0			0			0		1.82634	+	1.82634i		0		5.78485				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
145.e	even	4	1	inner
145.j	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2900.2.s.e	yes	40
5.b	even	2	1	inner	2900.2.s.e	yes	40
5.c	odd	4	2		2900.2.j.e	✓	40
29.c	odd	4	1		2900.2.j.e	✓	40
145.e	even	4	1	inner	2900.2.s.e	yes	40
145.f	odd	4	1		2900.2.j.e	✓	40
145.j	even	4	1	inner	2900.2.s.e	yes	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2900.2.j.e	✓	40	5.c	odd	4	2
2900.2.j.e	✓	40	29.c	odd	4	1
2900.2.j.e	✓	40	145.f	odd	4	1
2900.2.s.e	yes	40	1.a	even	1	1	trivial
2900.2.s.e	yes	40	5.b	even	2	1	inner
2900.2.s.e	yes	40	145.e	even	4	1	inner
2900.2.s.e	yes	40	145.j	even	4	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T3^20 - 36*T3^18 + 534*T3^16 - 4224*T3^14 + 19263*T3^12 - 51044*T3^10 + 75087*T3^8 - 54912*T3^6 + 16479*T3^4 - 1362*T3^2 + 1