Newform orbit 900.2.w.c

• Label: 900.2.w.c
• Level: $900$
• Weight: $2$
• Character orbit: 900.w
• Analytic conductor: $7.187$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.18653618192\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{10})\)
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{5}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
109.1		0			0			0		−2.23394	+	0.0974182i		0			−	1.31873i		0			0			0
109.2		0			0			0		−0.971442	+	2.01403i		0			−	1.04684i		0			0			0
109.3		0			0			0		−0.913250	−	2.04107i		0			−	4.62675i		0			0			0
109.4		0			0			0		1.64247	−	1.51733i		0				3.78808i		0			0			0
109.5		0			0			0		1.98828	+	1.02311i		0			−	3.54704i		0			0			0
109.6		0			0			0		2.10592	−	0.751722i		0				0.595901i		0			0			0
289.1		0			0			0		−2.23394	−	0.0974182i		0				1.31873i		0			0			0
289.2		0			0			0		−0.971442	−	2.01403i		0				1.04684i		0			0			0
289.3		0			0			0		−0.913250	+	2.04107i		0				4.62675i		0			0			0
289.4		0			0			0		1.64247	+	1.51733i		0			−	3.78808i		0			0			0
289.5		0			0			0		1.98828	−	1.02311i		0				3.54704i		0			0			0
289.6		0			0			0		2.10592	+	0.751722i		0			−	0.595901i		0			0			0
469.1		0			0			0		−1.99921	−	1.00158i		0			−	3.80992i		0			0			0
469.2		0			0			0		−1.28878	−	1.82730i		0				2.44380i		0			0			0
469.3		0			0			0		−0.892889	+	2.05006i		0			−	4.13266i		0			0			0
469.4		0			0			0		0.900274	+	2.04683i		0				0.957526i		0			0			0
469.5		0			0			0		0.921600	+	2.03732i		0				4.41540i		0			0			0
469.6		0			0			0		1.74098	−	1.40321i		0				1.57893i		0			0			0
829.1		0			0			0		−1.99921	+	1.00158i		0				3.80992i		0			0			0
829.2		0			0			0		−1.28878	+	1.82730i		0			−	2.44380i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.e	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	900.2.w.c		24
3.b	odd	2	1		300.2.o.a	✓	24
15.d	odd	2	1		1500.2.o.c		24
15.e	even	4	1		1500.2.m.c		24
15.e	even	4	1		1500.2.m.d		24
25.e	even	10	1	inner	900.2.w.c		24
75.h	odd	10	1		300.2.o.a	✓	24
75.h	odd	10	1		7500.2.d.g		24
75.j	odd	10	1		1500.2.o.c		24
75.j	odd	10	1		7500.2.d.g		24
75.l	even	20	1		1500.2.m.c		24
75.l	even	20	1		1500.2.m.d		24
75.l	even	20	1		7500.2.a.m		12
75.l	even	20	1		7500.2.a.n		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
300.2.o.a	✓	24	3.b	odd	2	1
300.2.o.a	✓	24	75.h	odd	10	1
900.2.w.c		24	1.a	even	1	1	trivial
900.2.w.c		24	25.e	even	10	1	inner
1500.2.m.c		24	15.e	even	4	1
1500.2.m.c		24	75.l	even	20	1
1500.2.m.d		24	15.e	even	4	1
1500.2.m.d		24	75.l	even	20	1
1500.2.o.c		24	15.d	odd	2	1
1500.2.o.c		24	75.j	odd	10	1
7500.2.a.m		12	75.l	even	20	1
7500.2.a.n		12	75.l	even	20	1
7500.2.d.g		24	75.h	odd	10	1
7500.2.d.g		24	75.j	odd	10	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^24 + 112*T7^22 + 5396*T7^20 + 146190*T7^18 + 2444070*T7^16 + 26062572*T7^14 + 177495989*T7^12 + 757283742*T7^10 + 1964246465*T7^8 + 2998987920*T7^6 + 2559664096*T7^4 + 1093572352*T7^2 + 172554496