Space of modular forms of level 175, weight 9, and Character 175.c

• Label: 175.9.c
• Level: $175$
• Weight: $9$
• Character orbit: 175.c
• Rep. character: $\chi_{175}(174,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(180\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(175, [\chi])\).

	Total	New	Old
Modular forms	166	98	68
Cusp forms	154	94	60
Eisenstein series	12	4	8

Trace form

94 * q - 11772 * q^4 + 215582 * q^9 + 26204 * q^11 - 71756 * q^14 + 1421996 * q^16 - 518172 * q^21 - 3946508 * q^29 - 30256092 * q^36 + 11477796 * q^39 - 28225974 * q^44 + 4012606 * q^46 + 13567514 * q^49 + 2906796 * q^51 + 66284266 * q^56 - 187278178 * q^64 - 186597616 * q^71 + 94195154 * q^74 + 288136612 * q^79 + 941529910 * q^81 - 76822272 * q^84 - 582097154 * q^86 - 64965612 * q^91 + 857810008 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.9.c.a	$175$	$9$	175.c	35.c	$2$	$2$	$2$	$71.291$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-7}) \)					7.9.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+31 i q^{2}-705 q^{4}-2401 i q^{7}+\cdots\)
175.9.c.b	$175$	$9$	175.c	35.c	$2$	$4$	$4$	$71.291$	\(\Q(i, \sqrt{21})\)	\(\Q(\sqrt{-7}) \)		✓			175.9.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-15\beta _{1}+\beta _{2})q^{2}+(-47+31\beta _{3})q^{4}+\cdots\)
175.9.c.c	$175$	$9$	175.c	35.c	$2$	$8$	$8$	$71.291$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					7.9.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{2}-\beta _{3})q^{2}+\beta _{4}q^{3}+(8+2^{4}\beta _{1}+\cdots)q^{4}+\cdots\)
175.9.c.d	$175$	$9$	175.c	35.c	$2$	$40$	$40$	$71.291$		None		✓			175.9.d.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
175.9.c.e	$175$	$9$	175.c	35.c	$2$	$40$	$40$	$71.291$		None					35.9.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)