Space of modular forms of level 575, weight 2, and Character 575.s

• Label: 575.2.s
• Level: $575$
• Weight: $2$
• Character orbit: 575.s
• Rep. character: $\chi_{575}(6,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $2320$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.s (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 575 \)
Character field:			\(\Q(\zeta_{55})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).

	Total	New	Old
Modular forms	2480	2480	0
Cusp forms	2320	2320	0
Eisenstein series	160	160	0

Trace form

2320 * q - 27 * q^2 - 31 * q^3 + 29 * q^4 - 30 * q^5 - 35 * q^6 - 76 * q^7 - 35 * q^8 + 23 * q^9 - 40 * q^10 - 29 * q^11 - 23 * q^12 - 35 * q^13 - 23 * q^14 - 13 * q^15 + 17 * q^16 - 21 * q^17 - 20 * q^18 - 23 * q^19 - 30 * q^20 - 17 * q^21 - 14 * q^22 - 88 * q^23 - 196 * q^24 + 12 * q^25 - 100 * q^26 - 37 * q^27 + 29 * q^28 - 15 * q^29 + 76 * q^30 - 39 * q^31 - 116 * q^32 - 9 * q^33 - 75 * q^34 - 8 * q^35 - 11 * q^36 + 33 * q^37 - 51 * q^38 - 15 * q^39 - 54 * q^40 - 27 * q^41 + 169 * q^42 - 44 * q^43 - 43 * q^44 - 134 * q^45 - 42 * q^46 - 200 * q^47 - 27 * q^48 - 276 * q^49 - 24 * q^50 - 20 * q^51 - 279 * q^52 - 55 * q^53 + 37 * q^54 - 52 * q^55 - 69 * q^56 - 60 * q^57 - 67 * q^58 + 3 * q^59 - 40 * q^60 - 43 * q^61 - 13 * q^62 + 29 * q^63 + 13 * q^64 - 23 * q^65 - 21 * q^66 - 73 * q^67 - 252 * q^68 - 189 * q^69 + 24 * q^70 + 75 * q^71 - 196 * q^72 + q^73 - 272 * q^75 + 42 * q^76 - 29 * q^77 + 65 * q^78 - 31 * q^79 + 37 * q^80 - 339 * q^81 - 40 * q^82 - 57 * q^83 - 21 * q^84 + 42 * q^85 - 329 * q^86 + 29 * q^87 - 83 * q^88 - 71 * q^89 + 187 * q^90 + 146 * q^91 - 21 * q^92 - 96 * q^93 - 27 * q^94 - 275 * q^95 + 201 * q^96 - 3 * q^97 + 93 * q^98 + 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
575.2.s.a	$575$	$2$	575.s	575.s	$55$	$2320$	$58$	$4.591$		None		✓	✓	✓	575.2.s.a	$4$	$0$	\(-27\)	\(-31\)	\(-30\)	\(-76\)		$\mathrm{SU}(2)[C_{55}]$