Space of modular forms of level 1360, weight 2, and Character 1360.o

• Label: 1360.2.o
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.o
• Rep. character: $\chi_{1360}(849,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $7$
• Sturm bound: $432$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1360, [\chi])\).

	Total	New	Old
Modular forms	228	56	172
Cusp forms	204	52	152
Eisenstein series	24	4	20

Trace form

\( 52 q + 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1360, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1360.2.o.a	$1360$	$2$	1360.o	85.c	$2$	$2$	$2$	$10.860$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(2-i)q^{5}-2q^{7}-2q^{9}+iq^{13}+\cdots\)
1360.2.o.b	$1360$	$2$	1360.o	85.c	$2$	$2$	$2$	$10.860$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-2-i)q^{5}+2q^{7}-2q^{9}+\cdots\)
1360.2.o.c	$1360$	$2$	1360.o	85.c	$2$	$4$	$4$	$10.860$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
1360.2.o.d	$1360$	$2$	1360.o	85.c	$2$	$4$	$4$	$10.860$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{8}^{3}q^{3}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}-3\zeta_{8}^{3}q^{7}+\cdots\)
1360.2.o.e	$1360$	$2$	1360.o	85.c	$2$	$8$	$8$	$10.860$	8.0.\(\cdots\).4	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{9}+\cdots\)
1360.2.o.f	$1360$	$2$	1360.o	85.c	$2$	$8$	$8$	$10.860$	8.0.\(\cdots\).11	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
1360.2.o.g	$1360$	$2$	1360.o	85.c	$2$	$24$	$24$	$10.860$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1360, [\chi]) \cong \)