Space of modular forms of level 175, weight 4, and Character 175.o

• Label: 175.4.o
• Level: $175$
• Weight: $4$
• Character orbit: 175.o
• Rep. character: $\chi_{175}(68,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $136$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).

	Total	New	Old
Modular forms	264	152	112
Cusp forms	216	136	80
Eisenstein series	48	16	32

Trace form

\( 136 q + 2 q^{2} + 6 q^{3} - 4 q^{7} + 124 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.4.o.a	$175$	$4$	175.o	35.k	$12$	$32$	$8$	$10.325$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
175.4.o.b	$175$	$4$	175.o	35.k	$12$	$40$	$10$	$10.325$		None		$4$	$0$	\(2\)	\(6\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$
175.4.o.c	$175$	$4$	175.o	35.k	$12$	$64$	$16$	$10.325$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)