Space of modular forms of level 175, weight 3, and Character 175.c

• Label: 175.3.c
• Level: $175$
• Weight: $3$
• Character orbit: 175.c
• Rep. character: $\chi_{175}(174,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $60$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	175.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(60\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(175, [\chi])\).

	Total	New	Old
Modular forms	46	26	20
Cusp forms	34	22	12
Eisenstein series	12	4	8

Trace form

\( 22 q - 36 q^{4} + 86 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(175, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.3.c.a	$175$	$3$	175.c	35.c	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3iq^{2}-5q^{4}+7iq^{7}-3iq^{8}-9q^{9}+\cdots\)
175.3.c.b	$175$	$3$	175.c	35.c	$2$	$4$	$4$	$4.768$	\(\Q(i, \sqrt{21})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-5+3\beta _{3})q^{4}+7\beta _{2}q^{7}+\cdots\)
175.3.c.c	$175$	$3$	175.c	35.c	$2$	$4$	$4$	$4.768$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{6}+(-\beta _{1}+3\beta _{3})q^{7}+\cdots\)
175.3.c.d	$175$	$3$	175.c	35.c	$2$	$4$	$4$	$4.768$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+3q^{4}+\beta _{2}q^{6}-7\beta _{1}q^{7}+\cdots\)
175.3.c.e	$175$	$3$	175.c	35.c	$2$	$8$	$8$	$4.768$	8.0.\(\cdots\).11	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(-3+2\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)