Space of modular forms of level 475, weight 3, and Character 475.d

• Label: 475.3.d
• Level: $475$
• Weight: $3$
• Character orbit: 475.d
• Rep. character: $\chi_{475}(474,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $4$
• Sturm bound: $150$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(150\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(475, [\chi])\).

	Total	New	Old
Modular forms	106	62	44
Cusp forms	94	58	36
Eisenstein series	12	4	8

Trace form

\( 58 q + 108 q^{4} - 12 q^{6} + 166 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
475.3.d.a	$475$	$3$	475.d	95.d	$2$	$2$	$2$	$12.943$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{4}-iq^{7}-9q^{9}+3q^{11}+2^{4}q^{16}+\cdots\)
475.3.d.b	$475$	$3$	475.d	95.d	$2$	$4$	$4$	$12.943$	\(\Q(i, \sqrt{13})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{3}q^{3}+9q^{4}+13q^{6}+\beta _{1}q^{7}+\cdots\)
475.3.d.c	$475$	$3$	475.d	95.d	$2$	$24$	$24$	$12.943$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
475.3.d.d	$475$	$3$	475.d	95.d	$2$	$28$	$28$	$12.943$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)