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

• Label: 675.2.ba
• Level: $675$
• Weight: $2$
• Character orbit: 675.ba
• Rep. character: $\chi_{675}(32,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $624$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 135 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	1152	672	480
Cusp forms	1008	624	384
Eisenstein series	144	48	96

Trace form

\( 624 q + 12 q^{2} + 12 q^{3} + 12 q^{7} + 18 q^{8} + O(q^{10}) \)

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.ba.a	$675$	$2$	675.ba	135.q	$36$	$144$	$12$	$5.390$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
675.2.ba.b	$675$	$2$	675.ba	135.q	$36$	$192$	$16$	$5.390$		None		$4$	$0$	\(12\)	\(12\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{36}]$
675.2.ba.c	$675$	$2$	675.ba	135.q	$36$	$288$	$24$	$5.390$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)