Space of modular forms of level 1100, weight 1, and Character 1100.f

• Label: 1100.1.f
• Level: $1100$
• Weight: $1$
• Character orbit: 1100.f
• Rep. character: $\chi_{1100}(901,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1100.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1100, [\chi])\).

	Total	New	Old
Modular forms	27	3	24
Cusp forms	9	3	6
Eisenstein series	18	0	18

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + q^{3} + 4 q^{9} - q^{11} + q^{23} - q^{27} + q^{31} + q^{33} + q^{37} - 2 q^{47} + 3 q^{49} - 2 q^{53} + q^{59} + q^{67} - 5 q^{69} - 3 q^{71} + q^{81} - 3 q^{89} - q^{93} + q^{97} - 4 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.1.f.a	$1100$	$1$	1100.f	11.b	$2$	$1$	$1$	$0.549$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None	✓				44.1.d.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}+q^{11}+q^{23}-q^{27}-q^{31}+\cdots\)
1100.1.f.b	$1100$	$1$	1100.f	11.b	$2$	$2$	$2$	$0.549$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None	✓		✓		220.1.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{3}+2q^{9}-q^{11}+\beta q^{23}-\beta q^{27}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1100, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)