Space of modular forms of level 755, weight 2, and Character 755.bc

• Label: 755.2.bc
• Level: $755$
• Weight: $2$
• Character orbit: 755.bc
• Rep. character: $\chi_{755}(11,\cdot)$
• Character field: $\Q(\zeta_{75})$
• Dimension: $2000$
• Newform subspaces: $2$
• Sturm bound: $152$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.bc (of order \(75\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 151 \)
Character field:			\(\Q(\zeta_{75})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(152\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(755, [\chi])\).

	Total	New	Old
Modular forms	3120	2000	1120
Cusp forms	2960	2000	960
Eisenstein series	160	0	160

Trace form

\( 2000 q + 240 q^{4} + 10 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(755, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
755.2.bc.a	$755$	$2$	755.bc	151.k	$75$	$1000$	$25$	$6.029$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{75}]$
755.2.bc.b	$755$	$2$	755.bc	151.k	$75$	$1000$	$25$	$6.029$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{75}]$

Decomposition of \(S_{2}^{\mathrm{old}}(755, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(151, [\chi])\)\(^{\oplus 2}\)