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

• Label: 3360.2.ba
• Level: $3360$
• Weight: $2$
• Character orbit: 3360.ba
• Rep. character: $\chi_{3360}(2591,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $1536$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3360.ba (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1536\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	800	96	704
Cusp forms	736	96	640
Eisenstein series	64	0	64

Trace form

\( 96 q + 16 q^{9} + O(q^{10}) \)

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.ba.a	$3360$	$2$	3360.ba	12.b	$2$	$4$	$4$	$26.830$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+\zeta_{8}q^{7}+\cdots\)
3360.2.ba.b	$3360$	$2$	3360.ba	12.b	$2$	$4$	$4$	$26.830$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}-\zeta_{8}q^{7}+(-1+\cdots)q^{9}+\cdots\)
3360.2.ba.c	$3360$	$2$	3360.ba	12.b	$2$	$20$	$20$	$26.830$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{11}q^{3}-\beta _{7}q^{5}+\beta _{7}q^{7}-\beta _{19}q^{9}+\cdots\)
3360.2.ba.d	$3360$	$2$	3360.ba	12.b	$2$	$20$	$20$	$26.830$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{3}-\beta _{7}q^{5}-\beta _{7}q^{7}-\beta _{19}q^{9}+\cdots\)
3360.2.ba.e	$3360$	$2$	3360.ba	12.b	$2$	$24$	$24$	$26.830$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
3360.2.ba.f	$3360$	$2$	3360.ba	12.b	$2$	$24$	$24$	$26.830$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)