Space of modular forms of level 175, weight 2, and Character 175.h

• Label: 175.2.h
• Level: $175$
• Weight: $2$
• Character orbit: 175.h
• Rep. character: $\chi_{175}(36,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).

	Total	New	Old
Modular forms	88	64	24
Cusp forms	72	64	8
Eisenstein series	16	0	16

Trace form

64 * q - 2 * q^2 - 4 * q^3 - 18 * q^4 + 4 * q^5 - 6 * q^8 - 24 * q^9 - 14 * q^10 - 8 * q^11 + 8 * q^12 - 24 * q^13 - 4 * q^14 + 2 * q^15 + 2 * q^16 - 16 * q^17 + 4 * q^18 + 12 * q^19 + 8 * q^20 - 4 * q^21 + 26 * q^22 - 6 * q^23 - 28 * q^24 + 22 * q^25 - 32 * q^26 + 2 * q^27 - 22 * q^29 - 32 * q^30 - 12 * q^31 + 16 * q^32 - 16 * q^33 + 30 * q^34 - 2 * q^35 - 16 * q^36 + 28 * q^37 - 10 * q^38 - 4 * q^39 + 64 * q^40 - 24 * q^41 + 30 * q^42 - 44 * q^43 + 22 * q^44 - 10 * q^45 + 4 * q^46 + 38 * q^47 + 78 * q^48 + 64 * q^49 - 4 * q^50 + 44 * q^51 - 92 * q^52 - 34 * q^53 + 54 * q^54 + 6 * q^55 - 12 * q^56 - 68 * q^57 + 66 * q^58 - 6 * q^59 + 12 * q^60 - 16 * q^61 - 46 * q^62 + 12 * q^63 - 6 * q^64 + 60 * q^65 + 74 * q^66 + 2 * q^67 - 116 * q^68 - 18 * q^69 - 16 * q^70 - 32 * q^71 - 50 * q^72 - 28 * q^73 + 40 * q^74 - 100 * q^75 - 52 * q^76 + 12 * q^77 + 142 * q^78 - 14 * q^80 + 2 * q^81 - 28 * q^82 - 74 * q^83 - 12 * q^84 + 38 * q^85 + 20 * q^86 + 82 * q^87 - 44 * q^88 + 28 * q^89 - 202 * q^90 - 8 * q^91 + 8 * q^92 + 16 * q^93 + 48 * q^94 + 58 * q^95 - 12 * q^96 - 58 * q^97 - 2 * q^98 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.2.h.a	$175$	$2$	175.h	25.d	$5$	$4$	$1$	$1.397$	\(\Q(\zeta_{10})\)	None		✓			175.2.h.a	$2$	$1$	\(-5\)	\(-4\)	\(-5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
175.2.h.b	$175$	$2$	175.h	25.d	$5$	$28$	$7$	$1.397$		None		✓			175.2.h.b	$2$	$0$	\(6\)	\(4\)	\(8\)	\(-28\)		$\mathrm{SU}(2)[C_{5}]$
175.2.h.c	$175$	$2$	175.h	25.d	$5$	$32$	$8$	$1.397$		None		✓	✓		175.2.h.c	$2$	$0$	\(-3\)	\(-4\)	\(1\)	\(32\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)