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

• Label: 2700.1.m
• Level: $2700$
• Weight: $1$
• Character orbit: 2700.m
• Rep. character: $\chi_{2700}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $540$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2700.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(540\)
Trace bound:			\(16\)

Dimensions

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

	Total	New	Old
Modular forms	124	16	108
Cusp forms	52	16	36
Eisenstein series	72	0	72

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + O(q^{10}) \)

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.m.a	$2700$	$1$	2700.m	60.l	$4$	$8$	$4$	$1.347$	\(\Q(\zeta_{24})\)	$D_{6}$	None	\(\Q(\sqrt{3}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$		\(q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{3}q^{8}+\cdots\)
2700.1.m.b	$2700$	$1$	2700.m	60.l	$4$	$8$	$4$	$1.347$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-15}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{3}q^{8}+\zeta_{24}^{4}q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2700, [\chi]) \cong \)