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

• Label: 1360.2.e
• Level: $1360$
• Weight: $2$
• Character orbit: 1360.e
• Rep. character: $\chi_{1360}(1089,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $432$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	228	48	180
Cusp forms	204	48	156
Eisenstein series	24	0	24

Trace form

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

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.e.a	$1360$	$2$	1360.e	5.b	$2$	$2$	$2$	$10.860$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1-2i)q^{5}-4iq^{7}+2q^{9}+\cdots\)
1360.2.e.b	$1360$	$2$	1360.e	5.b	$2$	$2$	$2$	$10.860$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1-2i)q^{5}+2q^{9}+6q^{11}+\cdots\)
1360.2.e.c	$1360$	$2$	1360.e	5.b	$2$	$6$	$6$	$10.860$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1360.2.e.d	$1360$	$2$	1360.e	5.b	$2$	$8$	$8$	$10.860$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6})q^{3}+\cdots\)
1360.2.e.e	$1360$	$2$	1360.e	5.b	$2$	$8$	$8$	$10.860$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+(-\beta _{2}+\beta _{5}-\beta _{7})q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots\)
1360.2.e.f	$1360$	$2$	1360.e	5.b	$2$	$10$	$10$	$10.860$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(\beta _{6}-\beta _{8})q^{5}+(\beta _{5}+\beta _{7})q^{7}+\cdots\)
1360.2.e.g	$1360$	$2$	1360.e	5.b	$2$	$12$	$12$	$10.860$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{6}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(680, [\chi])\)\(^{\oplus 2}\)