Space of modular forms of level 1760, weight 2, and Character 1760.l

• Label: 1760.2.l
• Level: $1760$
• Weight: $2$
• Character orbit: 1760.l
• Rep. character: $\chi_{1760}(529,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $576$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1760.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(576\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1760, [\chi])\).

	Total	New	Old
Modular forms	304	60	244
Cusp forms	272	60	212
Eisenstein series	32	0	32

Trace form

\( 60 q + 60 q^{9} + 4 q^{25} + 40 q^{31} - 8 q^{41} - 60 q^{49} - 24 q^{65} - 72 q^{71} + 16 q^{79} + 44 q^{81} - 56 q^{89} - 24 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1760, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1760.2.l.a	$1760$	$2$	1760.l	40.f	$2$	$2$	$2$	$14.054$	\(\Q(\sqrt{-1}) \)	None					440.2.l.a	$2$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{3}+(2 i+1)q^{5}+4 i q^{7}+q^{9}+\cdots\)
1760.2.l.b	$1760$	$2$	1760.l	40.f	$2$	$2$	$2$	$14.054$	\(\Q(\sqrt{-1}) \)	None					440.2.l.a	$2$	$0$	\(0\)	\(4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{3}+(2 i-1)q^{5}-4 i q^{7}+q^{9}+\cdots\)
1760.2.l.c	$1760$	$2$	1760.l	40.f	$2$	$56$	$56$	$14.054$		None			✓		440.2.l.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1760, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)