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

• Label: 575.2.r
• Level: $575$
• Weight: $2$
• Character orbit: 575.r
• Rep. character: $\chi_{575}(7,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $680$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.r (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	1320	760	560
Cusp forms	1080	680	400
Eisenstein series	240	80	160

Trace form

680 * q + 18 * q^2 + 14 * q^3 - 36 * q^6 + 22 * q^7 + 26 * q^8 - 44 * q^11 + 6 * q^12 + 26 * q^13 + 68 * q^16 + 22 * q^17 - 58 * q^18 - 44 * q^21 - 22 * q^23 - 52 * q^26 + 26 * q^27 - 66 * q^28 - 28 * q^31 + 46 * q^32 - 228 * q^36 - 66 * q^37 + 22 * q^38 - 92 * q^41 - 198 * q^42 + 22 * q^43 - 28 * q^46 - 52 * q^47 - 18 * q^48 - 44 * q^51 - 158 * q^52 + 22 * q^53 - 308 * q^56 - 66 * q^57 + 58 * q^58 - 220 * q^61 - 38 * q^62 + 22 * q^63 - 396 * q^66 + 22 * q^67 + 168 * q^71 + 28 * q^72 - 34 * q^73 - 396 * q^76 + 10 * q^77 - 22 * q^78 + 120 * q^81 + 50 * q^82 + 22 * q^83 - 132 * q^86 + 46 * q^87 + 110 * q^88 - 50 * q^92 + 36 * q^93 + 412 * q^96 + 88 * q^97 + 50 * 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.r.a	$575$	$2$	575.r	115.l	$44$	$160$	$8$	$4.591$		None		✓			575.2.r.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{44}]$
575.2.r.b	$575$	$2$	575.r	115.l	$44$	$200$	$10$	$4.591$		None					115.2.l.a	$4$	$0$	\(18\)	\(14\)	\(0\)	\(22\)		$\mathrm{SU}(2)[C_{44}]$
575.2.r.c	$575$	$2$	575.r	115.l	$44$	$320$	$16$	$4.591$		None		✓	✓		575.2.r.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{44}]$

Decomposition of \(S_{2}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)