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

• Label: 175.4.f
• Level: $175$
• Weight: $4$
• Character orbit: 175.f
• Rep. character: $\chi_{175}(118,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $8$
• Sturm bound: $80$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(80\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	132	76	56
Cusp forms	108	68	40
Eisenstein series	24	8	16

Trace form

\( 68 q + 4 q^{2} + 10 q^{7} - 112 q^{8} + O(q^{10}) \)

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.f.a	$175$	$4$	175.f	35.f	$4$	$4$	$2$	$10.325$	\(\Q(i, \sqrt{110})\)	None		$4$	$0$	\(-12\)	\(0\)	\(0\)	\(-48\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-3+3\beta _{2})q^{2}-\beta _{3}q^{3}-10\beta _{2}q^{4}+\cdots\)
175.4.f.b	$175$	$4$	175.f	35.f	$4$	$4$	$2$	$10.325$	\(\Q(i, \sqrt{14})\)	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{4}-7\beta _{1}q^{7}-9\beta _{3}q^{8}+\cdots\)
175.4.f.c	$175$	$4$	175.f	35.f	$4$	$4$	$2$	$10.325$	\(\Q(i, \sqrt{14})\)	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+2\beta _{1}q^{3}-8\beta _{2}q^{4}+7\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots\)
175.4.f.d	$175$	$4$	175.f	35.f	$4$	$4$	$2$	$10.325$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(42\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2\beta _{2})q^{2}+(-1+\beta _{2}+2\beta _{3})q^{3}+\cdots\)
175.4.f.e	$175$	$4$	175.f	35.f	$4$	$4$	$2$	$10.325$	\(\Q(i, \sqrt{110})\)	None		$4$	$0$	\(12\)	\(0\)	\(0\)	\(48\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(3+3\beta _{2})q^{2}+\beta _{1}q^{3}+10\beta _{2}q^{4}+\cdots\)
175.4.f.f	$175$	$4$	175.f	35.f	$4$	$8$	$4$	$10.325$	8.0.\(\cdots\).1	\(\Q(\sqrt{-7}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{4}$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{3}q^{2}+(13\beta _{1}+\beta _{7})q^{4}+7\beta _{2}q^{7}+\cdots\)
175.4.f.g	$175$	$4$	175.f	35.f	$4$	$16$	$8$	$10.325$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-32\)	$2^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{2}+\beta _{11}q^{3}+(-4\beta _{4}+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)
175.4.f.h	$175$	$4$	175.f	35.f	$4$	$24$	$12$	$10.325$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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