Space of modular forms of level 1100, weight 3, and Character 1100.f

• Label: 1100.3.f
• Level: $1100$
• Weight: $3$
• Character orbit: 1100.f
• Rep. character: $\chi_{1100}(901,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $6$
• Sturm bound: $540$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1100.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(540\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1100, [\chi])\).

	Total	New	Old
Modular forms	378	38	340
Cusp forms	342	38	304
Eisenstein series	36	0	36

Trace form

\( 38 q + 3 q^{3} + 101 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.3.f.a	$1100$	$3$	1100.f	11.b	$2$	$2$	$2$	$29.973$	\(\Q(\sqrt{33}) \)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-5\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2-\beta )q^{3}+(3+5\beta )q^{9}-11q^{11}+\cdots\)
1100.3.f.b	$1100$	$3$	1100.f	11.b	$2$	$4$	$4$	$29.973$	\(\Q(\sqrt{3}, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(13+\beta _{3})q^{9}+11q^{11}+(5\beta _{1}+\cdots)q^{23}+\cdots\)
1100.3.f.c	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{3}-\beta _{1}q^{7}+(2+\beta _{3})q^{9}+\cdots\)
1100.3.f.d	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+\beta _{4}q^{7}+(-3-\beta _{1})q^{9}+(-5+\cdots)q^{11}+\cdots\)
1100.3.f.e	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{3}+\beta _{1}q^{7}+(2+\beta _{3})q^{9}+\cdots\)
1100.3.f.f	$1100$	$3$	1100.f	11.b	$2$	$8$	$8$	$29.973$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{3}-\beta _{4}q^{7}+(4+\beta _{1}-\beta _{7})q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1100, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)