Space of modular forms of level 750, weight 2, and Character 750.r

• Label: 750.2.r
• Level: $750$
• Weight: $2$
• Character orbit: 750.r
• Rep. character: $\chi_{750}(17,\cdot)$
• Character field: $\Q(\zeta_{100})$
• Dimension: $2000$
• Newform subspaces: $1$
• Sturm bound: $300$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.r (of order \(100\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 375 \)
Character field:			\(\Q(\zeta_{100})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(300\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(750, [\chi])\).

	Total	New	Old
Modular forms	6160	2000	4160
Cusp forms	5840	2000	3840
Eisenstein series	320	0	320

Trace form

2000 * q + 40 * q^19 + 40 * q^22 + 120 * q^25 + 20 * q^28 + 40 * q^34 + 40 * q^39 + 80 * q^45 + 80 * q^57 - 20 * q^60 - 60 * q^63 - 80 * q^67 - 140 * q^69 - 80 * q^70 - 80 * q^73 - 160 * q^75 - 100 * q^78 - 80 * q^79 - 80 * q^82 - 60 * q^84 - 40 * q^85 - 100 * q^87 - 60 * q^90 - 20 * q^93 + 20 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(750, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
750.2.r.a	$750$	$2$	750.r	375.r	$100$	$2000$	$50$	$5.989$		None		✓	✓	✓	750.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{100}]$

Decomposition of \(S_{2}^{\mathrm{old}}(750, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(750, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)