Space of modular forms of level 675, weight 2, and Character 675.bi

• Label: 675.2.bi
• Level: $675$
• Weight: $2$
• Character orbit: 675.bi
• Rep. character: $\chi_{675}(2,\cdot)$
• Character field: $\Q(\zeta_{180})$
• Dimension: $4224$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.bi (of order \(180\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 675 \)
Character field:			\(\Q(\zeta_{180})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

	Total	New	Old
Modular forms	4416	4416	0
Cusp forms	4224	4224	0
Eisenstein series	192	192	0

Trace form

\( 4224 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 48 q^{7} - 72 q^{8} - 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.2.bi.a	$675$	$2$	675.bi	675.ai	$180$	$4224$	$88$	$5.390$		None		$4$	$0$	\(-48\)	\(-48\)	\(-48\)	\(-48\)		$\mathrm{SU}(2)[C_{180}]$