Space of modular forms of level 3360, weight 2, and Character 3360.z

• Label: 3360.2.z
• Level: $3360$
• Weight: $2$
• Character orbit: 3360.z
• Rep. character: $\chi_{3360}(1231,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $1536$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3360.z (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1536\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).

	Total	New	Old
Modular forms	800	64	736
Cusp forms	736	64	672
Eisenstein series	64	0	64

Trace form

\( 64 q - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3360.2.z.a	$3360$	$2$	3360.z	56.e	$2$	$4$	$4$	$26.830$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{2})q^{7}-q^{9}+\cdots\)
3360.2.z.b	$3360$	$2$	3360.z	56.e	$2$	$4$	$4$	$26.830$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+q^{5}+(1-\beta _{2})q^{7}-q^{9}-2q^{11}+\cdots\)
3360.2.z.c	$3360$	$2$	3360.z	56.e	$2$	$28$	$28$	$26.830$		None		$2$	$0$	\(0\)	\(0\)	\(-28\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$
3360.2.z.d	$3360$	$2$	3360.z	56.e	$2$	$28$	$28$	$26.830$		None		$2$	$0$	\(0\)	\(0\)	\(28\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)