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

• Label: 575.2.p
• Level: $575$
• Weight: $2$
• Character orbit: 575.p
• Rep. character: $\chi_{575}(49,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $340$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	660	380	280
Cusp forms	540	340	200
Eisenstein series	120	40	80

Trace form

340 * q + 58 * q^4 - 26 * q^6 + 52 * q^9 - 14 * q^11 + 18 * q^14 - 62 * q^16 + 26 * q^19 - 30 * q^21 + 52 * q^24 + 2 * q^26 + 38 * q^29 - 42 * q^31 - 18 * q^34 - 46 * q^36 - 66 * q^39 - 70 * q^41 + 80 * q^44 - 26 * q^46 - 44 * q^49 - 38 * q^51 - 234 * q^54 + 190 * q^56 - 98 * q^59 + 6 * q^61 - 94 * q^64 + 104 * q^66 + 140 * q^69 - 112 * q^71 - 126 * q^74 + 16 * q^76 - 58 * q^79 - 232 * q^81 - 178 * q^84 - 130 * q^86 + 78 * q^89 - 196 * q^91 + 126 * q^94 - 300 * q^96 + 16 * 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.p.a	$575$	$2$	575.p	115.j	$22$	$20$	$2$	$4.591$	\(\Q(\zeta_{44})\)	None					115.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{22}]$	\(q+(-\zeta_{44}^{3}+\zeta_{44}^{5}+\zeta_{44}^{9}+\zeta_{44}^{13}+\cdots)q^{2}+\cdots\)
575.2.p.b	$575$	$2$	575.p	115.j	$22$	$20$	$2$	$4.591$	\(\Q(\zeta_{44})\)	None					23.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{22}]$	\(q+(-\zeta_{44}-\zeta_{44}^{5}+\zeta_{44}^{7}+\zeta_{44}^{11}+\cdots)q^{2}+\cdots\)
575.2.p.c	$575$	$2$	575.p	115.j	$22$	$40$	$4$	$4.591$		None					115.2.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
575.2.p.d	$575$	$2$	575.p	115.j	$22$	$100$	$10$	$4.591$		None					115.2.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
575.2.p.e	$575$	$2$	575.p	115.j	$22$	$160$	$16$	$4.591$		None		✓	✓		575.2.k.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

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

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