Space of modular forms of level 3600, weight 1, and Character 3600.ct

• Label: 3600.1.ct
• Level: $3600$
• Weight: $1$
• Character orbit: 3600.ct
• Rep. character: $\chi_{3600}(559,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $720$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3600.ct (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(720\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).

	Total	New	Old
Modular forms	136	4	132
Cusp forms	40	4	36
Eisenstein series	96	0	96

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

\( 4 q - q^{5} - q^{25} + 2 q^{29} - 5 q^{37} - 2 q^{41} - 4 q^{49} + 5 q^{53} + 2 q^{61} + 5 q^{65} + 5 q^{85} - 3 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3600, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3600.1.ct.a	$3600$	$1$	3600.ct	100.h	$10$	$4$	$1$	$1.797$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	400.1.x.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{10}^{4}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3600, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)