Space of modular forms of level 1011, weight 1, and Character 1011.c

• Label: 1011.1.c
• Level: $1011$
• Weight: $1$
• Character orbit: 1011.c
• Rep. character: $\chi_{1011}(1010,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1011.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1011 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1011, [\chi])\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	5	5	0
Eisenstein series	2	2	0

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

\( 5 q - q^{3} + 5 q^{4} - 2 q^{7} + 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1011, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1011.1.c.a	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1011}) \)	\(\Q(\sqrt{337}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)	$1$		\(q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots\)
1011.1.c.b	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1011}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1011.1.c.c	$1011$	$1$	1011.c	1011.c	$2$	$1$	$1$	$0.505$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1011}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1011.1.c.d	$1011$	$1$	1011.c	1011.c	$2$	$2$	$2$	$0.505$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1011}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$		\(q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots\)