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

• Label: 3600.1.cc
• Level: $3600$
• Weight: $1$
• Character orbit: 3600.cc
• Rep. character: $\chi_{3600}(751,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $720$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3600.cc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(720\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	88	4	84
Cusp forms	16	4	12
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	4	0	0	0

Trace form

\( 4 q - 2 q^{9} - 2 q^{29} - 2 q^{41} + 4 q^{49} - 2 q^{61} + 6 q^{69} - 2 q^{81} + 4 q^{89}+O(q^{100}) \)

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.cc.a	$3600$	$1$	3600.cc	36.f	$6$	$2$	$1$	$1.797$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None					720.1.bu.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)	$1$		\(q-\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3600.1.cc.b	$3600$	$1$	3600.cc	36.f	$6$	$2$	$1$	$1.797$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-5}) \)	None					720.1.bu.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(3\)	$1$		\(q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots\)

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

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