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

• Label: 775.2.e
• Level: $775$
• Weight: $2$
• Character orbit: 775.e
• Rep. character: $\chi_{775}(501,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $160$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(160\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	172	108	64
Cusp forms	148	96	52
Eisenstein series	24	12	12

Trace form

\( 96 q + 4 q^{2} + 92 q^{4} - 4 q^{6} + 4 q^{7} + 24 q^{8} - 44 q^{9} + O(q^{10}) \)

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.e.a	$775$	$2$	775.e	31.c	$3$	$2$	$1$	$6.188$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-4\)	\(2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2q^{2}+(2-2\zeta_{6})q^{3}+2q^{4}+(-4+\cdots)q^{6}+\cdots\)
775.2.e.b	$775$	$2$	775.e	31.c	$3$	$2$	$1$	$6.188$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(4\)	\(2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2q^{2}+(2-2\zeta_{6})q^{3}+2q^{4}+(4-4\zeta_{6})q^{6}+\cdots\)
775.2.e.c	$775$	$2$	775.e	31.c	$3$	$4$	$2$	$6.188$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
775.2.e.d	$775$	$2$	775.e	31.c	$3$	$4$	$2$	$6.188$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(2\)	\(3\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
775.2.e.e	$775$	$2$	775.e	31.c	$3$	$4$	$2$	$6.188$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(4\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
775.2.e.f	$775$	$2$	775.e	31.c	$3$	$8$	$4$	$6.188$	8.0.42575625.1	None		$2$	$0$	\(-2\)	\(1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}+(-1-\beta _{1}+2\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
775.2.e.g	$775$	$2$	775.e	31.c	$3$	$8$	$4$	$6.188$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(2\)	\(-3\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
775.2.e.h	$775$	$2$	775.e	31.c	$3$	$18$	$9$	$6.188$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+\beta _{14}q^{3}+(1-\beta _{2})q^{4}+(\beta _{13}+\cdots)q^{6}+\cdots\)
775.2.e.i	$775$	$2$	775.e	31.c	$3$	$18$	$9$	$6.188$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{2}+(-\beta _{5}+\beta _{14})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
775.2.e.j	$775$	$2$	775.e	31.c	$3$	$28$	$14$	$6.188$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)