Space of modular forms of level 5780, weight 2, and Character 5780.c

• Label: 5780.2.c
• Level: $5780$
• Weight: $2$
• Character orbit: 5780.c
• Rep. character: $\chi_{5780}(5201,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $10$
• Sturm bound: $1836$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5780.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1836\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5780, [\chi])\).

	Total	New	Old
Modular forms	972	90	882
Cusp forms	864	90	774
Eisenstein series	108	0	108

Trace form

\( 90 q - 82 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5780, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5780.2.c.a	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{5}+2iq^{7}-q^{9}+2q^{13}+\cdots\)
5780.2.c.b	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{5}-2iq^{7}-q^{9}-5iq^{11}+\cdots\)
5780.2.c.c	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}+4iq^{7}+3q^{9}-2iq^{11}-6q^{13}+\cdots\)
5780.2.c.d	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}-2iq^{7}+3q^{9}+iq^{11}-3q^{19}+\cdots\)
5780.2.c.e	$5780$	$2$	5780.c	17.b	$2$	$4$	$4$	$46.154$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
5780.2.c.f	$5780$	$2$	5780.c	17.b	$2$	$6$	$6$	$46.154$	6.0.2611456.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots\)
5780.2.c.g	$5780$	$2$	5780.c	17.b	$2$	$12$	$12$	$46.154$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{11}q^{3}-\beta _{3}q^{5}-\beta _{6}q^{7}+\beta _{8}q^{9}+\cdots\)
5780.2.c.h	$5780$	$2$	5780.c	17.b	$2$	$12$	$12$	$46.154$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}-\beta _{6}q^{5}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)
5780.2.c.i	$5780$	$2$	5780.c	17.b	$2$	$24$	$24$	$46.154$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
5780.2.c.j	$5780$	$2$	5780.c	17.b	$2$	$24$	$24$	$46.154$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5780, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5780, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1445, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2890, [\chi])\)\(^{\oplus 2}\)