Space of modular forms of level 550, weight 2, and Character 550.b

• Label: 550.2.b
• Level: $550$
• Weight: $2$
• Character orbit: 550.b
• Rep. character: $\chi_{550}(199,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $6$
• Sturm bound: $180$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(180\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).

	Total	New	Old
Modular forms	102	14	88
Cusp forms	78	14	64
Eisenstein series	24	0	24

Trace form

14 * q - 14 * q^4 + 8 * q^6 - 14 * q^9 - 2 * q^11 + 14 * q^16 + 8 * q^19 - 16 * q^21 - 8 * q^24 - 24 * q^26 + 4 * q^29 - 4 * q^31 + 28 * q^34 + 14 * q^36 - 8 * q^39 + 44 * q^41 + 2 * q^44 + 24 * q^46 - 38 * q^49 - 32 * q^51 - 32 * q^54 - 32 * q^59 + 12 * q^61 - 14 * q^64 - 8 * q^66 + 48 * q^69 + 4 * q^71 + 12 * q^74 - 8 * q^76 + 24 * q^79 + 14 * q^81 + 16 * q^84 + 4 * q^86 + 24 * q^89 - 56 * q^91 + 8 * q^94 + 8 * q^96 + 26 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
550.2.b.a	$550$	$2$	550.b	5.b	$2$	$2$	$2$	$4.392$	\(\Q(\sqrt{-1}) \)	None					110.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots\)
550.2.b.b	$550$	$2$	550.b	5.b	$2$	$2$	$2$	$4.392$	\(\Q(\sqrt{-1}) \)	None					110.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-5 i q^{7}+\cdots\)
550.2.b.c	$550$	$2$	550.b	5.b	$2$	$2$	$2$	$4.392$	\(\Q(\sqrt{-1}) \)	None					110.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}-i q^{7}+\cdots\)
550.2.b.d	$550$	$2$	550.b	5.b	$2$	$2$	$2$	$4.392$	\(\Q(\sqrt{-1}) \)	None		✓			550.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}+4 i q^{7}+\cdots\)
550.2.b.e	$550$	$2$	550.b	5.b	$2$	$2$	$2$	$4.392$	\(\Q(\sqrt{-1}) \)	None		✓			550.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}-i q^{8}+\cdots\)
550.2.b.f	$550$	$2$	550.b	5.b	$2$	$4$	$4$	$4.392$	\(\Q(i, \sqrt{33})\)	None			✓		110.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

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