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

• Label: 1760.2.f
• Level: $1760$
• Weight: $2$
• Character orbit: 1760.f
• Rep. character: $\chi_{1760}(351,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $33$

Defining parameters

Level:	\( N \)	\(=\)	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1760.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(33\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	304	48	256
Cusp forms	272	48	224
Eisenstein series	32	0	32

Trace form

\( 48 q - 64 q^{9} + 48 q^{25} + 16 q^{33} + 32 q^{49} + 32 q^{53} - 64 q^{69} - 16 q^{77} + 48 q^{81} + 16 q^{89} + 64 q^{93} + 32 q^{97}+O(q^{100}) \)

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.f.a	$1760$	$2$	1760.f	44.c	$2$	$4$	$4$	$14.054$	\(\Q(\zeta_{8})\)	None		✓			1760.2.f.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}-\beta_1)q^{3}+q^{5}+(-\beta_{2}-\beta_1)q^{7}+\cdots\)
1760.2.f.b	$1760$	$2$	1760.f	44.c	$2$	$4$	$4$	$14.054$	\(\Q(\zeta_{8})\)	None		✓			1760.2.f.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}-\beta_1)q^{3}+q^{5}-q^{9}+(-\beta_{2}+2\beta_1)q^{11}+\cdots\)
1760.2.f.c	$1760$	$2$	1760.f	44.c	$2$	$16$	$16$	$14.054$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1760.2.f.c	$4$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+q^{5}+\beta _{9}q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots\)
1760.2.f.d	$1760$	$2$	1760.f	44.c	$2$	$24$	$24$	$14.054$		None		✓	✓		1760.2.f.d	$4$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1760, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)