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

• Label: 575.2.w
• Level: $575$
• Weight: $2$
• Character orbit: 575.w
• Rep. character: $\chi_{575}(17,\cdot)$
• Character field: $\Q(\zeta_{220})$
• Dimension: $4640$
• 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.w (of order \(220\) and degree \(80\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 575 \)
Character field:			\(\Q(\zeta_{220})\)
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	4960	4960	0
Cusp forms	4640	4640	0
Eisenstein series	320	320	0

Trace form

4640 * q - 72 * q^2 - 76 * q^3 - 90 * q^4 - 88 * q^5 - 54 * q^6 - 88 * q^7 - 64 * q^8 - 90 * q^9 - 88 * q^10 - 66 * q^11 - 84 * q^12 - 64 * q^13 - 110 * q^14 - 88 * q^15 - 158 * q^16 - 88 * q^17 - 148 * q^18 - 110 * q^19 - 88 * q^20 - 66 * q^21 + 78 * q^23 - 140 * q^25 - 144 * q^26 - 124 * q^27 - 176 * q^28 - 50 * q^29 - 88 * q^30 - 54 * q^31 - 44 * q^32 - 110 * q^33 - 110 * q^34 - 56 * q^35 + 74 * q^36 - 176 * q^37 - 88 * q^38 - 170 * q^39 - 88 * q^40 - 54 * q^41 - 308 * q^42 - 88 * q^43 - 110 * q^44 - 60 * q^46 + 148 * q^47 + 332 * q^48 - 188 * q^50 - 176 * q^51 - 28 * q^52 - 88 * q^53 + 170 * q^54 - 40 * q^55 - 66 * q^56 - 176 * q^57 - 32 * q^58 - 190 * q^59 - 88 * q^60 - 66 * q^61 - 228 * q^62 - 88 * q^63 - 90 * q^64 - 88 * q^65 - 66 * q^66 - 88 * q^67 - 30 * q^69 - 392 * q^70 - 234 * q^71 + 208 * q^72 - 44 * q^73 - 48 * q^75 - 176 * q^76 - 252 * q^78 - 110 * q^79 - 286 * q^80 - 178 * q^81 - 200 * q^82 - 88 * q^83 - 110 * q^84 - 292 * q^85 - 66 * q^86 + 116 * q^87 - 110 * q^89 - 506 * q^90 - 10 * q^92 - 424 * q^93 - 90 * q^94 + 562 * q^95 + 74 * q^96 - 22 * q^97 - 220 * q^98

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.w.a	$575$	$2$	575.w	575.w	$220$	$4640$	$58$	$4.591$		None		✓	✓	✓	575.2.w.a	$4$	$0$	\(-72\)	\(-76\)	\(-88\)	\(-88\)		$\mathrm{SU}(2)[C_{220}]$