Space of modular forms of level 2700, weight 1, and Character 2700.ca

• Label: 2700.1.ca
• Level: $2700$
• Weight: $1$
• Character orbit: 2700.ca
• Rep. character: $\chi_{2700}(407,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $540$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2700.ca (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 540 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(540\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2700, [\chi])\).

	Total	New	Old
Modular forms	168	72	96
Cusp forms	24	24	0
Eisenstein series	144	48	96

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 12 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2700.1.ca.a	$2700$	$1$	2700.ca	540.ag	$36$	$24$	$2$	$1.347$	\(\Q(\zeta_{72})\)	$D_{18}$	\(\Q(\sqrt{-5}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{72}^{29}q^{2}+\zeta_{72}^{19}q^{3}-\zeta_{72}^{22}q^{4}+\cdots\)