Space of modular forms of level 900, weight 1, and Character 900.x

• Label: 900.1.x
• Level: $900$
• Weight: $1$
• Character orbit: 900.x
• Rep. character: $\chi_{900}(91,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	900.x (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(900, [\chi])\).

	Total	New	Old
Modular forms	48	12	36
Cusp forms	16	4	12
Eisenstein series	32	8	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + q^{2} - q^{4} + q^{5} + q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(900, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
900.1.x.a	$900$	$1$	900.x	100.j	$10$	$4$	$1$	$0.449$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)