Newform orbit 900.2.bk.a

• Label: 900.2.bk.a
• Level: $900$
• Weight: $2$
• Character orbit: 900.bk
• Analytic conductor: $7.187$
• Analytic rank: $0$
• Dimension: $80$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bk (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.18653618192\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(10\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 8 q^{7} - 12 q^{13} - 40 q^{19} + 16 q^{25} + 12 q^{37} + 24 q^{55} + 48 q^{67} + 52 q^{73} + 80 q^{79} + 92 q^{85} + 28 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		0			0			0		−1.94151	−	1.10930i		0		2.98378	+	2.98378i		0			0			0
17.2		0			0			0		−1.76258	−	1.37598i		0		−2.64913	−	2.64913i		0			0			0
17.3		0			0			0		−1.55058	+	1.61112i		0		−0.783791	−	0.783791i		0			0			0
17.4		0			0			0		−1.25100	+	1.85337i		0		−1.44431	−	1.44431i		0			0			0
17.5		0			0			0		−1.07182	−	1.96245i		0		1.45099	+	1.45099i		0			0			0
17.6		0			0			0		1.07182	+	1.96245i		0		1.45099	+	1.45099i		0			0			0
17.7		0			0			0		1.25100	−	1.85337i		0		−1.44431	−	1.44431i		0			0			0
17.8		0			0			0		1.55058	−	1.61112i		0		−0.783791	−	0.783791i		0			0			0
17.9		0			0			0		1.76258	+	1.37598i		0		−2.64913	−	2.64913i		0			0			0
17.10		0			0			0		1.94151	+	1.10930i		0		2.98378	+	2.98378i		0			0			0
53.1		0			0			0		−1.94151	+	1.10930i		0		2.98378	−	2.98378i		0			0			0
53.2		0			0			0		−1.76258	+	1.37598i		0		−2.64913	+	2.64913i		0			0			0
53.3		0			0			0		−1.55058	−	1.61112i		0		−0.783791	+	0.783791i		0			0			0
53.4		0			0			0		−1.25100	−	1.85337i		0		−1.44431	+	1.44431i		0			0			0
53.5		0			0			0		−1.07182	+	1.96245i		0		1.45099	−	1.45099i		0			0			0
53.6		0			0			0		1.07182	−	1.96245i		0		1.45099	−	1.45099i		0			0			0
53.7		0			0			0		1.25100	+	1.85337i		0		−1.44431	+	1.44431i		0			0			0
53.8		0			0			0		1.55058	+	1.61112i		0		−0.783791	+	0.783791i		0			0			0
53.9		0			0			0		1.76258	−	1.37598i		0		−2.64913	+	2.64913i		0			0			0
53.10		0			0			0		1.94151	−	1.10930i		0		2.98378	−	2.98378i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
25.f	odd	20	1	inner
75.l	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	900.2.bk.a	✓	80
3.b	odd	2	1	inner	900.2.bk.a	✓	80
25.f	odd	20	1	inner	900.2.bk.a	✓	80
75.l	even	20	1	inner	900.2.bk.a	✓	80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
900.2.bk.a	✓	80	1.a	even	1	1	trivial
900.2.bk.a	✓	80	3.b	odd	2	1	inner
900.2.bk.a	✓	80	25.f	odd	20	1	inner
900.2.bk.a	✓	80	75.l	even	20	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(900, [\chi])\).