Newform orbit 900.2.n.d

• Label: 900.2.n.d
• Level: $900$
• Weight: $2$
• Character orbit: 900.n
• Analytic conductor: $7.187$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(7.18653618192\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{7} - 4 q^{13} + 2 q^{19} + 20 q^{25} - 6 q^{31} + 20 q^{37} + 64 q^{43} + 56 q^{49} + 10 q^{55} - 4 q^{61} + 52 q^{67} + 24 q^{79} + 70 q^{85} + 38 q^{91} - 68 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
181.1		0			0			0		−2.22936	−	0.173095i		0		−0.188502				0			0			0
181.2		0			0			0		−1.74470	−	1.39858i		0		4.13135				0			0			0
181.3		0			0			0		−0.420683	+	2.19614i		0		−2.94285				0			0			0
181.4		0			0			0		0.420683	−	2.19614i		0		−2.94285				0			0			0
181.5		0			0			0		1.74470	+	1.39858i		0		4.13135				0			0			0
181.6		0			0			0		2.22936	+	0.173095i		0		−0.188502				0			0			0
361.1		0			0			0		−2.22875	+	0.180798i		0		−2.37109				0			0			0
361.2		0			0			0		−2.08304	−	0.812982i		0		4.76222				0			0			0
361.3		0			0			0		−0.0514217	+	2.23548i		0		−1.39114				0			0			0
361.4		0			0			0		0.0514217	−	2.23548i		0		−1.39114				0			0			0
361.5		0			0			0		2.08304	+	0.812982i		0		4.76222				0			0			0
361.6		0			0			0		2.22875	−	0.180798i		0		−2.37109				0			0			0
541.1		0			0			0		−2.22875	−	0.180798i		0		−2.37109				0			0			0
541.2		0			0			0		−2.08304	+	0.812982i		0		4.76222				0			0			0
541.3		0			0			0		−0.0514217	−	2.23548i		0		−1.39114				0			0			0
541.4		0			0			0		0.0514217	+	2.23548i		0		−1.39114				0			0			0
541.5		0			0			0		2.08304	−	0.812982i		0		4.76222				0			0			0
541.6		0			0			0		2.22875	+	0.180798i		0		−2.37109				0			0			0
721.1		0			0			0		−2.22936	+	0.173095i		0		−0.188502				0			0			0
721.2		0			0			0		−1.74470	+	1.39858i		0		4.13135				0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
25.d	even	5	1	inner
75.j	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	900.2.n.d	✓	24
3.b	odd	2	1	inner	900.2.n.d	✓	24
25.d	even	5	1	inner	900.2.n.d	✓	24
75.j	odd	10	1	inner	900.2.n.d	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
900.2.n.d	✓	24	1.a	even	1	1	trivial
900.2.n.d	✓	24	3.b	odd	2	1	inner
900.2.n.d	✓	24	25.d	even	5	1	inner
900.2.n.d	✓	24	75.j	odd	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{6} - 2T_{7}^{5} - 26T_{7}^{4} + 9T_{7}^{3} + 199T_{7}^{2} + 228T_{7} + 36 \) acting on \(S_{2}^{\mathrm{new}}(900, [\chi])\).