Space of modular forms of level 3600, weight 2, and Character 3600.o

• Label: 3600.2.o
• Level: $3600$
• Weight: $2$
• Character orbit: 3600.o
• Rep. character: $\chi_{3600}(3599,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $1440$
• Trace bound: $77$

Defining parameters

Level:	\( N \)	\(=\)	\( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3600.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1440\)
Trace bound:			\(77\)
Distinguishing \(T_p\):			\(7\), \(137\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3600, [\chi])\).

	Total	New	Old
Modular forms	792	36	756
Cusp forms	648	36	612
Eisenstein series	144	0	144

Trace form

\( 36 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3600.2.o.a	$3600$	$2$	3600.o	60.h	$2$	$4$	$4$	$28.746$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+2\zeta_{8}q^{13}+\zeta_{8}^{3}q^{17}-\zeta_{8}^{2}q^{29}+\cdots\)
3600.2.o.b	$3600$	$2$	3600.o	60.h	$2$	$8$	$8$	$28.746$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}^{3}q^{7}-\zeta_{24}^{4}q^{11}-\zeta_{24}q^{13}+\cdots\)
3600.2.o.c	$3600$	$2$	3600.o	60.h	$2$	$8$	$8$	$28.746$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{3}q^{7}+(-\zeta_{24}^{2}-\zeta_{24}^{3})q^{11}+\cdots\)
3600.2.o.d	$3600$	$2$	3600.o	60.h	$2$	$8$	$8$	$28.746$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{3}q^{7}+(-\zeta_{24}^{2}+\zeta_{24}^{3})q^{11}+\cdots\)
3600.2.o.e	$3600$	$2$	3600.o	60.h	$2$	$8$	$8$	$28.746$	8.0.3317760000.4	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{7}-\beta _{7}q^{11}-\beta _{1}q^{13}+\beta _{4}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)