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

• Label: 575.2.b
• Level: $575$
• Weight: $2$
• Character orbit: 575.b
• Rep. character: $\chi_{575}(24,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $6$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
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	66	34	32
Cusp forms	54	34	20
Eisenstein series	12	0	12

Trace form

34 * q - 36 * q^4 + 4 * q^6 - 30 * q^9 - 8 * q^11 + 4 * q^14 + 40 * q^16 - 4 * q^19 + 8 * q^21 - 8 * q^24 - 24 * q^26 - 16 * q^29 + 20 * q^31 - 4 * q^34 + 24 * q^36 + 48 * q^41 + 52 * q^44 + 4 * q^46 - 66 * q^49 + 16 * q^51 + 36 * q^54 - 80 * q^56 - 12 * q^59 + 60 * q^61 - 60 * q^64 - 16 * q^66 - 8 * q^69 - 20 * q^71 - 28 * q^74 + 28 * q^76 - 8 * q^79 + 34 * q^81 + 68 * q^84 - 68 * q^86 - 56 * q^89 - 24 * q^91 - 60 * q^94 - 140 * q^96 + 116 * 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.b.a	$575$	$2$	575.b	5.b	$2$	$2$	$2$	$4.591$	\(\Q(\sqrt{-1}) \)	None					115.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}+i q^{7}+3 q^{9}+2 q^{11}+\cdots\)
575.2.b.b	$575$	$2$	575.b	5.b	$2$	$2$	$2$	$4.591$	\(\Q(\sqrt{-1}) \)	None		✓			575.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-i q^{7}+3 i q^{8}+3 q^{9}+\cdots\)
575.2.b.c	$575$	$2$	575.b	5.b	$2$	$4$	$4$	$4.591$	\(\Q(i, \sqrt{5})\)	None					115.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
575.2.b.d	$575$	$2$	575.b	5.b	$2$	$4$	$4$	$4.591$	\(\Q(i, \sqrt{5})\)	None					23.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
575.2.b.e	$575$	$2$	575.b	5.b	$2$	$8$	$8$	$4.591$	8.0.\(\cdots\).11	None					115.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
575.2.b.f	$575$	$2$	575.b	5.b	$2$	$14$	$14$	$4.591$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓		575.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots\)

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

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