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

• Label: 3360.2.g
• Level: $3360$
• Weight: $2$
• Character orbit: 3360.g
• Rep. character: $\chi_{3360}(1681,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $1536$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3360.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1536\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	800	48	752
Cusp forms	736	48	688
Eisenstein series	64	0	64

Trace form

\( 48 q + 8 q^{7} - 48 q^{9} + O(q^{10}) \)

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.g.a	$3360$	$2$	3360.g	8.b	$2$	$8$	$8$	$26.830$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}q^{3}+\zeta_{16}q^{5}-q^{7}-q^{9}-\zeta_{16}^{3}q^{11}+\cdots\)
3360.2.g.b	$3360$	$2$	3360.g	8.b	$2$	$12$	$12$	$26.830$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}-q^{9}-\beta _{6}q^{11}+\cdots\)
3360.2.g.c	$3360$	$2$	3360.g	8.b	$2$	$12$	$12$	$26.830$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}-q^{9}+\beta _{5}q^{11}+\cdots\)
3360.2.g.d	$3360$	$2$	3360.g	8.b	$2$	$16$	$16$	$26.830$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{1}q^{5}+q^{7}-q^{9}+\beta _{8}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)