Space of modular forms of level 1775, weight 1, and Character 1775.bb

• Label: 1775.1.bb
• Level: $1775$
• Weight: $1$
• Character orbit: 1775.bb
• Rep. character: $\chi_{1775}(354,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1775.bb (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1775 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1775, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	28	0	0	0

Trace form

\( 28 q + 7 q^{4} + 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1775, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1775.1.bb.a	$1775$	$1$	1775.bb	1775.ab	$10$	$4$	$1$	$0.886$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(5\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(1-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{2})q^{3}+\cdots\)
1775.1.bb.b	$1775$	$1$	1775.bb	1775.ab	$10$	$24$	$6$	$0.886$	\(\Q(\zeta_{35})\)	$D_{70}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(-5\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{70}^{17}-\zeta_{70}^{25})q^{2}+(-\zeta_{70}^{23}+\cdots)q^{3}+\cdots\)