Space of modular forms of level 751, weight 2, and Character 751.k

• Label: 751.2.k
• Level: $751$
• Weight: $2$
• Character orbit: 751.k
• Rep. character: $\chi_{751}(32,\cdot)$
• Character field: $\Q(\zeta_{75})$
• Dimension: $2480$
• Newform subspaces: $1$
• Sturm bound: $125$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	751.k (of order \(75\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 751 \)
Character field:			\(\Q(\zeta_{75})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(125\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(751, [\chi])\).

	Total	New	Old
Modular forms	2560	2560	0
Cusp forms	2480	2480	0
Eisenstein series	80	80	0

Trace form

\( 2480 q - 20 q^{2} - 45 q^{3} - 20 q^{4} - 40 q^{5} - 20 q^{6} - 40 q^{7} - 80 q^{8} - 45 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(751, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
751.2.k.a	$751$	$2$	751.k	751.k	$75$	$2480$	$62$	$5.997$		None		$2$	$0$	\(-20\)	\(-45\)	\(-40\)	\(-40\)		$\mathrm{SU}(2)[C_{75}]$