Newform orbit 475.3.d.c

• Label: 475.3.d.c
• Level: $475$
• Weight: $3$
• Character orbit: 475.d
• Analytic conductor: $12.943$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(12.9428125571\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
474.1	−3.38208			4.08851			7.43849				0		−13.8277					4.56923i	−11.6293			7.71590				0
474.2	−3.38208			4.08851			7.43849				0		−13.8277				−	4.56923i	−11.6293			7.71590				0
474.3	−2.84623			2.18419			4.10101				0		−6.21669					9.15076i	−0.287487			−4.22932				0
474.4	−2.84623			2.18419			4.10101				0		−6.21669				−	9.15076i	−0.287487			−4.22932				0
474.5	−2.36559			−3.55563			1.59600				0		8.41115					11.0785i	5.68687			3.64250				0
474.6	−2.36559			−3.55563			1.59600				0		8.41115				−	11.0785i	5.68687			3.64250				0
474.7	−1.88109			−0.840697			−0.461500				0		1.58143					2.31342i	8.39248			−8.29323				0
474.8	−1.88109			−0.840697			−0.461500				0		1.58143				−	2.31342i	8.39248			−8.29323				0
474.9	−1.14149			4.13699			−2.69701				0		−4.72232					7.54444i	7.64455			8.11468				0
474.10	−1.14149			4.13699			−2.69701				0		−4.72232				−	7.54444i	7.64455			8.11468				0
474.11	−0.151673			−5.10387			−3.97700				0		0.774118				−	6.35478i	1.20989			17.0495				0
474.12	−0.151673			−5.10387			−3.97700				0		0.774118					6.35478i	1.20989			17.0495				0
474.13	0.151673			5.10387			−3.97700				0		0.774118				−	6.35478i	−1.20989			17.0495				0
474.14	0.151673			5.10387			−3.97700				0		0.774118					6.35478i	−1.20989			17.0495				0
474.15	1.14149			−4.13699			−2.69701				0		−4.72232					7.54444i	−7.64455			8.11468				0
474.16	1.14149			−4.13699			−2.69701				0		−4.72232				−	7.54444i	−7.64455			8.11468				0
474.17	1.88109			0.840697			−0.461500				0		1.58143					2.31342i	−8.39248			−8.29323				0
474.18	1.88109			0.840697			−0.461500				0		1.58143				−	2.31342i	−8.39248			−8.29323				0
474.19	2.36559			3.55563			1.59600				0		8.41115					11.0785i	−5.68687			3.64250				0
474.20	2.36559			3.55563			1.59600				0		8.41115				−	11.0785i	−5.68687			3.64250				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.b	odd	2	1	inner
95.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	475.3.d.c		24
5.b	even	2	1	inner	475.3.d.c		24
5.c	odd	4	1		95.3.c.a	✓	12
5.c	odd	4	1		475.3.c.g		12
15.e	even	4	1		855.3.e.a		12
19.b	odd	2	1	inner	475.3.d.c		24
20.e	even	4	1		1520.3.h.a		12
95.d	odd	2	1	inner	475.3.d.c		24
95.g	even	4	1		95.3.c.a	✓	12
95.g	even	4	1		475.3.c.g		12
285.j	odd	4	1		855.3.e.a		12
380.j	odd	4	1		1520.3.h.a		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.3.c.a	✓	12	5.c	odd	4	1
95.3.c.a	✓	12	95.g	even	4	1
475.3.c.g		12	5.c	odd	4	1
475.3.c.g		12	95.g	even	4	1
475.3.d.c		24	1.a	even	1	1	trivial
475.3.d.c		24	5.b	even	2	1	inner
475.3.d.c		24	19.b	odd	2	1	inner
475.3.d.c		24	95.d	odd	2	1	inner
855.3.e.a		12	15.e	even	4	1
855.3.e.a		12	285.j	odd	4	1
1520.3.h.a		12	20.e	even	4	1
1520.3.h.a		12	380.j	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} - 30T_{2}^{10} + 329T_{2}^{8} - 1620T_{2}^{6} + 3479T_{2}^{4} - 2470T_{2}^{2} + 55 \) acting on \(S_{3}^{\mathrm{new}}(475, [\chi])\).