Space of modular forms of level 2200, weight 2, and Character 2200.b

• Label: 2200.2.b
• Level: $2200$
• Weight: $2$
• Character orbit: 2200.b
• Rep. character: $\chi_{2200}(1849,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $13$
• Sturm bound: $720$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2200.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(720\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2200, [\chi])\).

	Total	New	Old
Modular forms	384	46	338
Cusp forms	336	46	290
Eisenstein series	48	0	48

Trace form

\( 46 q - 42 q^{9} - 6 q^{11} + 16 q^{21} - 28 q^{29} - 16 q^{39} - 4 q^{41} - 30 q^{49} + 24 q^{51} + 20 q^{59} - 44 q^{61} - 20 q^{69} - 16 q^{71} + 40 q^{79} + 14 q^{81} - 52 q^{89} - 32 q^{91} + 18 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2200.2.b.a	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	\(\Q(\sqrt{-1}) \)	None					88.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-2 i q^{7}-6 q^{9}-q^{11}+\cdots\)
2200.2.b.b	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	\(\Q(\sqrt{-1}) \)	None					440.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-i q^{7}-6 q^{9}-q^{11}-6 i q^{13}+\cdots\)
2200.2.b.c	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	\(\Q(\sqrt{-1}) \)	None					440.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{7}+3 q^{9}-q^{11}-3\beta q^{13}+\cdots\)
2200.2.b.d	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	\(\Q(\sqrt{-1}) \)	None					440.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{7}+3 q^{9}-q^{11}+8 q^{19}-4\beta q^{23}+\cdots\)
2200.2.b.e	$2200$	$2$	2200.b	5.b	$2$	$2$	$2$	$17.567$	\(\Q(\sqrt{-1}) \)	None					440.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{7}+3 q^{9}+q^{11}+2\beta q^{13}-2\beta q^{17}+\cdots\)
2200.2.b.f	$2200$	$2$	2200.b	5.b	$2$	$4$	$4$	$17.567$	\(\Q(i, \sqrt{17})\)	None					440.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.g	$2200$	$2$	2200.b	5.b	$2$	$4$	$4$	$17.567$	\(\Q(i, \sqrt{17})\)	None					88.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.h	$2200$	$2$	2200.b	5.b	$2$	$4$	$4$	$17.567$	\(\Q(i, \sqrt{17})\)	None					440.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.i	$2200$	$2$	2200.b	5.b	$2$	$4$	$4$	$17.567$	\(\Q(i, \sqrt{17})\)	None					440.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+q^{11}+\cdots\)
2200.2.b.j	$2200$	$2$	2200.b	5.b	$2$	$4$	$4$	$17.567$	\(\Q(i, \sqrt{5})\)	None		✓			2200.2.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
2200.2.b.k	$2200$	$2$	2200.b	5.b	$2$	$4$	$4$	$17.567$	\(\Q(i, \sqrt{5})\)	None		✓			2200.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.b.l	$2200$	$2$	2200.b	5.b	$2$	$6$	$6$	$17.567$	6.0.44836416.1	None		✓			2200.2.a.t	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2200.2.b.m	$2200$	$2$	2200.b	5.b	$2$	$6$	$6$	$17.567$	6.0.96668224.1	None		✓			2200.2.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1100, [\chi])\)\(^{\oplus 2}\)