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

• Label: 775.2.b
• Level: $775$
• Weight: $2$
• Character orbit: 775.b
• Rep. character: $\chi_{775}(249,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $8$
• Sturm bound: $160$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(160\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	86	46	40
Cusp forms	74	46	28
Eisenstein series	12	0	12

Trace form

\( 46 q - 48 q^{4} - 8 q^{6} - 34 q^{9} + O(q^{10}) \)

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.b.a	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
775.2.b.b	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4iq^{7}+\cdots\)
775.2.b.c	$775$	$2$	775.b	5.b	$2$	$2$	$2$	$6.188$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2q^{4}+2q^{9}-4q^{11}-2iq^{12}+\cdots\)
775.2.b.d	$775$	$2$	775.b	5.b	$2$	$4$	$4$	$6.188$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+2\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
775.2.b.e	$775$	$2$	775.b	5.b	$2$	$8$	$8$	$6.188$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
775.2.b.f	$775$	$2$	775.b	5.b	$2$	$8$	$8$	$6.188$	8.0.4589249536.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{4})q^{4}+(-1+\cdots)q^{6}+\cdots\)
775.2.b.g	$775$	$2$	775.b	5.b	$2$	$10$	$10$	$6.188$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{8})q^{3}+(-1+\cdots)q^{4}+\cdots\)
775.2.b.h	$775$	$2$	775.b	5.b	$2$	$10$	$10$	$6.188$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{6}+\cdots)q^{4}+\cdots\)

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

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