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

• Label: 2700.1.be
• Level: $2700$
• Weight: $1$
• Character orbit: 2700.be
• Rep. character: $\chi_{2700}(143,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• 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.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{12})\)
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	24	144
Cusp forms	24	8	16
Eisenstein series	144	16	128

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 4 q^{16} + 12 q^{41} - 8 q^{46} - 12 q^{56} - 4 q^{61}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2700.1.be.a	$2700$	$1$	2700.be	180.v	$12$	$8$	$2$	$1.347$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None			✓	✓	900.1.bd.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{3}-\zeta_{24}^{11}+\cdots)q^{7}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2700, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)