Space of modular forms of level 770, weight 2, and Character 770.bd

• Label: 770.2.bd
• Level: $770$
• Weight: $2$
• Character orbit: 770.bd
• Rep. character: $\chi_{770}(263,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $192$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 385 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

	Total	New	Old
Modular forms	608	192	416
Cusp forms	544	192	352
Eisenstein series	64	0	64

Trace form

\( 192 q + 8 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
770.2.bd.a	$770$	$2$	770.bd	385.ac	$12$	$192$	$48$	$6.148$		None		$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)