Space of modular forms of level 1100, weight 2, and Character 1100.b

• Label: 1100.2.b
• Level: $1100$
• Weight: $2$
• Character orbit: 1100.b
• Rep. character: $\chi_{1100}(749,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $5$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1100, [\chi])\).

	Total	New	Old
Modular forms	198	14	184
Cusp forms	162	14	148
Eisenstein series	36	0	36

Trace form

14 * q - 20 * q^9 - 2 * q^11 - 4 * q^19 + 32 * q^21 + 4 * q^29 + 2 * q^31 + 28 * q^39 - 28 * q^41 - 26 * q^49 - 20 * q^51 + 58 * q^59 - 18 * q^69 + 22 * q^71 - 24 * q^79 + 14 * q^81 + 30 * q^89 - 20 * q^91 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.2.b.a	$1100$	$2$	1100.b	5.b	$2$	$2$	$2$	$8.784$	\(\Q(\sqrt{-1}) \)	None					220.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-2\beta q^{7}-q^{9}-q^{11}+2\beta q^{13}+\cdots\)
1100.2.b.b	$1100$	$2$	1100.b	5.b	$2$	$2$	$2$	$8.784$	\(\Q(\sqrt{-1}) \)	None					220.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-q^{9}+q^{11}+2\beta q^{17}+4 q^{19}+\cdots\)
1100.2.b.c	$1100$	$2$	1100.b	5.b	$2$	$2$	$2$	$8.784$	\(\Q(\sqrt{-1}) \)	None					44.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-2 i q^{7}+2 q^{9}-q^{11}-4 i q^{13}+\cdots\)
1100.2.b.d	$1100$	$2$	1100.b	5.b	$2$	$4$	$4$	$8.784$	\(\Q(i, \sqrt{21})\)	None		✓			1100.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
1100.2.b.e	$1100$	$2$	1100.b	5.b	$2$	$4$	$4$	$8.784$	\(\Q(i, \sqrt{13})\)	None		✓			1100.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)