Space of modular forms of level 175, weight 5, and Character 175.c

• Label: 175.5.c
• Level: $175$
• Weight: $5$
• Character orbit: 175.c
• Rep. character: $\chi_{175}(174,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(100\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(175, [\chi])\).

	Total	New	Old
Modular forms	86	50	36
Cusp forms	74	46	28
Eisenstein series	12	4	8

Trace form

\( 46 q - 348 q^{4} + 1142 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(175, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.5.c.a	$175$	$5$	175.c	35.c	$2$	$2$	$2$	$18.090$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{2}+15q^{4}+7^{2}iq^{7}+31iq^{8}+\cdots\)
175.5.c.b	$175$	$5$	175.c	35.c	$2$	$4$	$4$	$18.090$	\(\Q(i, \sqrt{21})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+(-2^{5}+\beta _{3})q^{4}-7^{2}\beta _{1}q^{7}+\cdots\)
175.5.c.c	$175$	$5$	175.c	35.c	$2$	$16$	$16$	$18.090$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}-\beta _{4}q^{4}+\beta _{5}q^{6}+\cdots\)
175.5.c.d	$175$	$5$	175.c	35.c	$2$	$24$	$24$	$18.090$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)