Space of modular forms of level 1776, weight 1, and Character 1776.n

• Label: 1776.1.n
• Level: $1776$
• Weight: $1$
• Character orbit: 1776.n
• Rep. character: $\chi_{1776}(1553,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $304$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1776.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(304\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1776, [\chi])\).

	Total	New	Old
Modular forms	38	7	31
Cusp forms	26	5	21
Eisenstein series	12	2	10

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	5	0	0	0

Trace form

\( 5 q + 2 q^{3} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1776, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1776.1.n.a	$1776$	$1$	1776.n	111.d	$2$	$1$	$1$	$0.886$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \)	\(\Q(\sqrt{37}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)	$1$		\(q-q^{3}+2q^{7}+q^{9}-2q^{21}-q^{25}+\cdots\)
1776.1.n.b	$1776$	$1$	1776.n	111.d	$2$	$2$	$2$	$0.886$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{37}) \)		$4$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{6}^{2}q^{3}-q^{7}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{11}+\cdots\)
1776.1.n.c	$1776$	$1$	1776.n	111.d	$2$	$2$	$2$	$0.886$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-111}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{15}+\beta q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1776, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1776, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 2}\)