Space of modular forms of level 1100, weight 6, and Character 1100.b

• Label: 1100.6.b
• Level: $1100$
• Weight: $6$
• Character orbit: 1100.b
• Rep. character: $\chi_{1100}(749,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $9$
• Sturm bound: $1080$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1100.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1080\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1100, [\chi])\).

	Total	New	Old
Modular forms	918	74	844
Cusp forms	882	74	808
Eisenstein series	36	0	36

Trace form

\( 74 q - 4972 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(1100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.6.b.a	$1100$	$6$	1100.b	5.b	$2$	$2$	$2$	$176.422$	\(\Q(\sqrt{-1}) \)	None					44.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+7iq^{3}+50iq^{7}+194q^{9}+11^{2}q^{11}+\cdots\)
1100.6.b.b	$1100$	$6$	1100.b	5.b	$2$	$4$	$4$	$176.422$	\(\Q(i, \sqrt{1761})\)	None					220.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-5\beta _{2})q^{3}+(5\beta _{1}+34\beta _{2})q^{7}+\cdots\)
1100.6.b.c	$1100$	$6$	1100.b	5.b	$2$	$4$	$4$	$176.422$	\(\Q(i, \sqrt{31})\)	None					44.6.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3\beta _{1}+\beta _{3})q^{3}+(-134\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1100.6.b.d	$1100$	$6$	1100.b	5.b	$2$	$6$	$6$	$176.422$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					220.6.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-24\beta _{3}+7\beta _{4}+2\beta _{5})q^{7}+\cdots\)
1100.6.b.e	$1100$	$6$	1100.b	5.b	$2$	$8$	$8$	$176.422$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					220.6.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-6\beta _{2}+\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots\)
1100.6.b.f	$1100$	$6$	1100.b	5.b	$2$	$8$	$8$	$176.422$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					220.6.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(3\beta _{1}-\beta _{2}-\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots\)
1100.6.b.g	$1100$	$6$	1100.b	5.b	$2$	$10$	$10$	$176.422$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					220.6.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(-\beta _{5}+2\beta _{6}+\beta _{8})q^{7}+(-94+\cdots)q^{9}+\cdots\)
1100.6.b.h	$1100$	$6$	1100.b	5.b	$2$	$16$	$16$	$176.422$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1100.6.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{2}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}+(-2\beta _{8}+4\beta _{9}-\beta _{10})q^{7}+\cdots\)
1100.6.b.i	$1100$	$6$	1100.b	5.b	$2$	$16$	$16$	$176.422$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1100.6.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{8}+\beta _{9})q^{3}+(-2\beta _{9}+\beta _{10})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1100, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)