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

• Label: 3600.1.da
• Level: $3600$
• Weight: $1$
• Character orbit: 3600.da
• Rep. character: $\chi_{3600}(1343,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• 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.da (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{12})\)
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	176	8	168
Cusp forms	32	8	24
Eisenstein series	144	0	144

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

\( 8 q + 8 q^{21} + 12 q^{41} + 4 q^{61} + 4 q^{81}+O(q^{100}) \)

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.da.a	$3600$	$1$	3600.da	180.v	$12$	$8$	$2$	$1.797$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None		✓	✓	✓	3600.1.da.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{7}-\zeta_{24}^{2}q^{9}+\cdots\)

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

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