Space of modular forms of level 175, weight 6, and Character 175.b

• Label: 175.6.b
• Level: $175$
• Weight: $6$
• Character orbit: 175.b
• Rep. character: $\chi_{175}(99,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $8$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(175, [\chi])\).

	Total	New	Old
Modular forms	106	46	60
Cusp forms	94	46	48
Eisenstein series	12	0	12

Trace form

\( 46 q - 728 q^{4} + 360 q^{6} - 3954 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(175, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.6.b.a	$175$	$6$	175.b	5.b	$2$	$2$	$2$	$28.067$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+10iq^{2}-14iq^{3}-68q^{4}+140q^{6}+\cdots\)
175.6.b.b	$175$	$6$	175.b	5.b	$2$	$2$	$2$	$28.067$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+8iq^{2}+iq^{3}-2^{5}q^{4}-8q^{6}-7^{2}iq^{7}+\cdots\)
175.6.b.c	$175$	$6$	175.b	5.b	$2$	$4$	$4$	$28.067$	\(\Q(i, \sqrt{57})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+5\beta _{2})q^{2}+(6\beta _{1}+6\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
175.6.b.d	$175$	$6$	175.b	5.b	$2$	$4$	$4$	$28.067$	\(\Q(i, \sqrt{65})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(3\beta _{1}+3\beta _{2})q^{3}+(15+\beta _{3})q^{4}+\cdots\)
175.6.b.e	$175$	$6$	175.b	5.b	$2$	$6$	$6$	$28.067$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{2})q^{2}+(-9\beta _{1}-\beta _{5})q^{3}+\cdots\)
175.6.b.f	$175$	$6$	175.b	5.b	$2$	$8$	$8$	$28.067$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}+\beta _{4})q^{2}+(-4\beta _{1}-\beta _{4}+\beta _{7})q^{3}+\cdots\)
175.6.b.g	$175$	$6$	175.b	5.b	$2$	$8$	$8$	$28.067$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3}+\beta _{6})q^{3}+(3+\cdots)q^{4}+\cdots\)
175.6.b.h	$175$	$6$	175.b	5.b	$2$	$12$	$12$	$28.067$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-2\beta _{8})q^{2}+(-\beta _{1}+3\beta _{8}-\beta _{10}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)