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

• Label: 575.2.m
• Level: $575$
• Weight: $2$
• Character orbit: 575.m
• Rep. character: $\chi_{575}(22,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $464$
• 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.m (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 575 \)
Character field:			\(\Q(\zeta_{20})\)
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	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

464 * q - 16 * q^2 - 12 * q^3 - 20 * q^4 - 12 * q^6 - 24 * q^8 - 20 * q^9 - 4 * q^12 - 24 * q^13 + 92 * q^16 - 28 * q^18 + 10 * q^23 + 52 * q^25 - 32 * q^26 + 36 * q^27 - 60 * q^29 - 12 * q^31 - 44 * q^32 - 32 * q^35 - 140 * q^36 + 60 * q^39 - 12 * q^41 - 6 * q^46 + 28 * q^47 - 244 * q^48 + 100 * q^50 - 280 * q^52 - 280 * q^54 - 48 * q^55 - 56 * q^58 + 80 * q^59 + 140 * q^62 - 20 * q^64 - 80 * q^69 + 216 * q^70 - 52 * q^71 - 32 * q^72 - 44 * q^73 - 128 * q^75 - 88 * q^77 + 164 * q^78 + 112 * q^81 + 112 * q^82 - 16 * q^85 - 204 * q^87 - 78 * q^92 + 248 * q^93 - 20 * q^94 + 76 * q^95 + 124 * q^96 + 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.m.a	$575$	$2$	575.m	575.m	$20$	$464$	$58$	$4.591$		None		✓	✓	✓	575.2.m.a	$4$	$0$	\(-16\)	\(-12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$