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

• Label: 475.3.c
• Level: $475$
• Weight: $3$
• Character orbit: 475.c
• Rep. character: $\chi_{475}(151,\cdot)$
• Character field: $\Q$
• Dimension: $61$
• Newform subspaces: $9$
• Sturm bound: $150$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(150\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	106	67	39
Cusp forms	94	61	33
Eisenstein series	12	6	6

Trace form

\( 61 q - 114 q^{4} - 18 q^{6} - 5 q^{7} - 157 q^{9} + O(q^{10}) \)

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.c.a	$475$	$3$	475.c	19.b	$2$	$1$	$1$	$12.943$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+5q^{7}+9q^{9}+3q^{11}+2^{4}q^{16}+\cdots\)
475.3.c.b	$475$	$3$	475.c	19.b	$2$	$2$	$2$	$12.943$	\(\Q(\sqrt{-13}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-9q^{4}+13q^{6}+5q^{7}+\cdots\)
475.3.c.c	$475$	$3$	475.c	19.b	$2$	$2$	$2$	$12.943$	\(\Q(\sqrt{19}) \)	\(\Q(\sqrt{-19}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}-3\beta q^{7}+9q^{9}-3q^{11}+2^{4}q^{16}+\cdots\)
475.3.c.d	$475$	$3$	475.c	19.b	$2$	$4$	$4$	$12.943$	4.0.7600.1	\(\Q(\sqrt{-95}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(-4+3\beta _{3})q^{4}+\cdots\)
475.3.c.e	$475$	$3$	475.c	19.b	$2$	$4$	$4$	$12.943$	4.0.462080.1	\(\Q(\sqrt{-95}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+\beta _{3})q^{4}+\cdots\)
475.3.c.f	$475$	$3$	475.c	19.b	$2$	$8$	$8$	$12.943$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+2\beta _{4})q^{4}+\cdots\)
475.3.c.g	$475$	$3$	475.c	19.b	$2$	$12$	$12$	$12.943$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
475.3.c.h	$475$	$3$	475.c	19.b	$2$	$14$	$14$	$12.943$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{6}+\cdots\)
475.3.c.i	$475$	$3$	475.c	19.b	$2$	$14$	$14$	$12.943$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{6}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)