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

• Label: 175.3.d
• Level: $175$
• Weight: $3$
• Character orbit: 175.d
• Rep. character: $\chi_{175}(76,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $10$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	175.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	46	29	17
Cusp forms	34	23	11
Eisenstein series	12	6	6

Trace form

\( 23 q + q^{2} + 49 q^{4} - 3 q^{7} + 5 q^{8} - 69 q^{9} + O(q^{10}) \)

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.d.a	$175$	$3$	175.d	7.b	$2$	$1$	$1$	$4.768$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(3\)	\(0\)	\(0\)	\(7\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{2}+5q^{4}+7q^{7}+3q^{8}+9q^{9}+\cdots\)
175.3.d.b	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{-10}) \)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{2}+\beta q^{3}+5q^{4}-3\beta q^{6}+(3+2\beta )q^{7}+\cdots\)
175.3.d.c	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+\beta q^{3}-2\beta q^{6}+(2-3\beta )q^{7}+\cdots\)
175.3.d.d	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{21}) \)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(14\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta )q^{2}+(2+3\beta )q^{4}+7q^{7}+\cdots\)
175.3.d.e	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-35}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{3}-4q^{4}-7iq^{7}+8q^{9}-13q^{11}+\cdots\)
175.3.d.f	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-14\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta q^{3}-3q^{4}+\beta q^{6}-7q^{7}+\cdots\)
175.3.d.g	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{21}) \)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-14\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta )q^{2}+(2+3\beta )q^{4}-7q^{7}+(13+\cdots)q^{8}+\cdots\)
175.3.d.h	$175$	$3$	175.d	7.b	$2$	$2$	$2$	$4.768$	\(\Q(\sqrt{-10}) \)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{2}+\beta q^{3}+5q^{4}+3\beta q^{6}+(-3+\cdots)q^{7}+\cdots\)
175.3.d.i	$175$	$3$	175.d	7.b	$2$	$4$	$4$	$4.768$	4.0.1163520.6	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(3-2\beta _{3})q^{4}+\cdots\)
175.3.d.j	$175$	$3$	175.d	7.b	$2$	$4$	$4$	$4.768$	4.0.1163520.6	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{2}-\beta _{1}q^{3}+(3-2\beta _{3})q^{4}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)