Space of modular forms of level 2775, weight 1, and Character 2775.b

• Label: 2775.1.b
• Level: $2775$
• Weight: $1$
• Character orbit: 2775.b
• Rep. character: $\chi_{2775}(2774,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $380$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2775 = 3 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2775.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 555 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(380\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2775, [\chi])\).

	Total	New	Old
Modular forms	34	10	24
Cusp forms	22	6	16
Eisenstein series	12	4	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 2 q^{4} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2775, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2775.1.b.a	$2775$	$1$	2775.b	555.b	$2$	$2$	$2$	$1.385$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \)	\(\Q(\sqrt{37}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{3}+q^{4}-iq^{7}-q^{9}-iq^{12}+\cdots\)
2775.1.b.b	$2775$	$1$	2775.b	555.b	$2$	$4$	$4$	$1.385$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-111}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2775, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2775, [\chi]) \cong \)