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

• Label: 3360.2.t
• Level: $3360$
• Weight: $2$
• Character orbit: 3360.t
• Rep. character: $\chi_{3360}(2689,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $14$
• Sturm bound: $1536$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3360.t (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1536\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(11\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	800	72	728
Cusp forms	736	72	664
Eisenstein series	64	0	64

Trace form

\( 72 q + 8 q^{5} - 72 q^{9} + O(q^{10}) \)

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.t.a	$3360$	$2$	3360.t	5.b	$2$	$2$	$2$	$26.830$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2-i)q^{5}+iq^{7}-q^{9}+\cdots\)
3360.2.t.b	$3360$	$2$	3360.t	5.b	$2$	$2$	$2$	$26.830$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-2-i)q^{5}-iq^{7}-q^{9}+\cdots\)
3360.2.t.c	$3360$	$2$	3360.t	5.b	$2$	$2$	$2$	$26.830$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(1-2i)q^{5}-iq^{7}-q^{9}-6q^{11}+\cdots\)
3360.2.t.d	$3360$	$2$	3360.t	5.b	$2$	$2$	$2$	$26.830$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1-2i)q^{5}+iq^{7}-q^{9}-2q^{11}+\cdots\)
3360.2.t.e	$3360$	$2$	3360.t	5.b	$2$	$2$	$2$	$26.830$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+2q^{11}+\cdots\)
3360.2.t.f	$3360$	$2$	3360.t	5.b	$2$	$2$	$2$	$26.830$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(1+2i)q^{5}-iq^{7}-q^{9}+6q^{11}+\cdots\)
3360.2.t.g	$3360$	$2$	3360.t	5.b	$2$	$4$	$4$	$26.830$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+2\beta _{2}q^{13}+\cdots\)
3360.2.t.h	$3360$	$2$	3360.t	5.b	$2$	$6$	$6$	$26.830$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
3360.2.t.i	$3360$	$2$	3360.t	5.b	$2$	$6$	$6$	$26.830$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
3360.2.t.j	$3360$	$2$	3360.t	5.b	$2$	$8$	$8$	$26.830$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{20}q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}q^{7}-q^{9}+\cdots\)
3360.2.t.k	$3360$	$2$	3360.t	5.b	$2$	$8$	$8$	$26.830$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{3}-\zeta_{24}^{6}q^{5}-\zeta_{24}q^{7}-q^{9}+\cdots\)
3360.2.t.l	$3360$	$2$	3360.t	5.b	$2$	$8$	$8$	$26.830$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{3}-\zeta_{24}^{3}q^{5}-\zeta_{24}q^{7}-q^{9}+\cdots\)
3360.2.t.m	$3360$	$2$	3360.t	5.b	$2$	$10$	$10$	$26.830$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
3360.2.t.n	$3360$	$2$	3360.t	5.b	$2$	$10$	$10$	$26.830$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)