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

• Label: 1760.2.c
• Level: $1760$
• Weight: $2$
• Character orbit: 1760.c
• Rep. character: $\chi_{1760}(879,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $3$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1760.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 440 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)
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	76	228
Cusp forms	272	68	204
Eisenstein series	32	8	24

Trace form

\( 68 q - 68 q^{9} + 4 q^{11} - 4 q^{25} - 52 q^{49} - 8 q^{59} + 24 q^{75} + 52 q^{81} - 8 q^{89} - 64 q^{91} - 4 q^{99}+O(q^{100}) \)

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.c.a	$1760$	$2$	1760.c	440.c	$2$	$4$	$4$	$14.054$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-10}) \)					440.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{5}+2\beta _{1}q^{7}+3q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
1760.2.c.b	$1760$	$2$	1760.c	440.c	$2$	$8$	$8$	$14.054$	8.0.\(\cdots\).19	\(\Q(\sqrt{-55}) \)					440.2.c.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}+3q^{9}+\beta _{3}q^{11}+\cdots\)
1760.2.c.c	$1760$	$2$	1760.c	440.c	$2$	$56$	$56$	$14.054$		None			✓		440.2.c.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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