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

• Label: 750.2.c
• Level: $750$
• Weight: $2$
• Character orbit: 750.c
• Rep. character: $\chi_{750}(499,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $300$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(300\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	170	16	154
Cusp forms	130	16	114
Eisenstein series	40	0	40

Trace form

\( 16 q - 16 q^{4} - 16 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
750.2.c.a	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+(\beta _{1}+4\beta _{3})q^{7}+\cdots\)
750.2.c.b	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}-q^{6}+2\beta _{1}q^{7}+\cdots\)
750.2.c.c	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
750.2.c.d	$750$	$2$	750.c	5.b	$2$	$4$	$4$	$5.989$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(750, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 2}\)