Space of modular forms of level 1100, weight 4, and Character 1100.b

• Label: 1100.4.b
• Level: $1100$
• Weight: $4$
• Character orbit: 1100.b
• Rep. character: $\chi_{1100}(749,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $10$
• Sturm bound: $720$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1100.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(720\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1100, [\chi])\).

	Total	New	Old
Modular forms	558	46	512
Cusp forms	522	46	476
Eisenstein series	36	0	36

Trace form

\( 46 q - 538 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.4.b.a	$1100$	$4$	1100.b	5.b	$2$	$2$	$2$	$64.902$	\(\Q(\sqrt{-1}) \)	None					220.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{3}-12iq^{7}-37q^{9}-11q^{11}+\cdots\)
1100.4.b.b	$1100$	$4$	1100.b	5.b	$2$	$2$	$2$	$64.902$	\(\Q(\sqrt{-1}) \)	None					220.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}+11iq^{7}+2q^{9}-11q^{11}+\cdots\)
1100.4.b.c	$1100$	$4$	1100.b	5.b	$2$	$2$	$2$	$64.902$	\(\Q(\sqrt{-1}) \)	None					44.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}-26iq^{7}+2q^{9}-11q^{11}+\cdots\)
1100.4.b.d	$1100$	$4$	1100.b	5.b	$2$	$2$	$2$	$64.902$	\(\Q(\sqrt{-1}) \)	None					220.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}+19iq^{7}+2q^{9}-11q^{11}+\cdots\)
1100.4.b.e	$1100$	$4$	1100.b	5.b	$2$	$4$	$4$	$64.902$	\(\Q(i, \sqrt{97})\)	None					44.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-2\beta _{2})q^{3}+(6\beta _{1}+4\beta _{2})q^{7}+(-22+\cdots)q^{9}+\cdots\)
1100.4.b.f	$1100$	$4$	1100.b	5.b	$2$	$4$	$4$	$64.902$	\(\Q(i, \sqrt{97})\)	None					220.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-2\beta _{2})q^{3}+(\beta _{1}+4\beta _{2})q^{7}+(-22+\cdots)q^{9}+\cdots\)
1100.4.b.g	$1100$	$4$	1100.b	5.b	$2$	$4$	$4$	$64.902$	\(\Q(i, \sqrt{6})\)	None					220.4.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}-\beta _{2})q^{3}+(9\beta _{1}-2\beta _{2})q^{7}+(-13+\cdots)q^{9}+\cdots\)
1100.4.b.h	$1100$	$4$	1100.b	5.b	$2$	$6$	$6$	$64.902$	6.0.1351885824.3	None					220.4.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
1100.4.b.i	$1100$	$4$	1100.b	5.b	$2$	$10$	$10$	$64.902$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1100.4.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(-12-\beta _{2})q^{9}+\cdots\)
1100.4.b.j	$1100$	$4$	1100.b	5.b	$2$	$10$	$10$	$64.902$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1100.4.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(\beta _{3}+2\beta _{6}-\beta _{7})q^{7}+(-12+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1100, [\chi])\) into lower level spaces

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