Space of modular forms of level 775, weight 2, and Character 775.bj

• Label: 775.2.bj
• Level: $775$
• Weight: $2$
• Character orbit: 775.bj
• Rep. character: $\chi_{775}(57,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $184$
• Newform subspaces: $7$
• Sturm bound: $160$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bj (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(160\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

	Total	New	Old
Modular forms	344	200	144
Cusp forms	296	184	112
Eisenstein series	48	16	32

Trace form

\( 184 q + 8 q^{2} + 6 q^{3} + 12 q^{6} + 6 q^{7} - 20 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
775.2.bj.a	$775$	$2$	775.bj	155.p	$12$	$4$	$1$	$6.188$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2-2\zeta_{12}+2\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{4}+\cdots\)
775.2.bj.b	$775$	$2$	775.bj	155.p	$12$	$4$	$1$	$6.188$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2+2\zeta_{12}-2\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{4}+\cdots\)
775.2.bj.c	$775$	$2$	775.bj	155.p	$12$	$4$	$1$	$6.188$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(4\)	\(6\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
775.2.bj.d	$775$	$2$	775.bj	155.p	$12$	$4$	$1$	$6.188$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(4\)	\(6\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
775.2.bj.e	$775$	$2$	775.bj	155.p	$12$	$32$	$8$	$6.188$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
775.2.bj.f	$775$	$2$	775.bj	155.p	$12$	$48$	$12$	$6.188$		None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{12}]$
775.2.bj.g	$775$	$2$	775.bj	155.p	$12$	$88$	$22$	$6.188$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)