Space of modular forms of level 550, weight 5, and Character 550.d

• Label: 550.5.d
• Level: $550$
• Weight: $5$
• Character orbit: 550.d
• Rep. character: $\chi_{550}(351,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $5$
• Sturm bound: $450$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	550.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(450\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(550, [\chi])\).

	Total	New	Old
Modular forms	372	76	296
Cusp forms	348	76	272
Eisenstein series	24	0	24

Trace form

\( 76 q - 18 q^{3} - 608 q^{4} + 2042 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(550, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
550.5.d.a	$550$	$5$	550.d	11.b	$2$	$4$	$4$	$56.853$	\(\Q(\sqrt{-2}, \sqrt{553})\)	None					22.5.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-8q^{4}-\beta _{3}q^{6}+12\beta _{2}q^{7}+\cdots\)
550.5.d.b	$550$	$5$	550.d	11.b	$2$	$16$	$16$	$56.853$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					110.5.d.a	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)	$2^{26}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-1+\beta _{2})q^{3}-8q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
550.5.d.c	$550$	$5$	550.d	11.b	$2$	$16$	$16$	$56.853$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			550.5.d.c	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-1-\beta _{1})q^{3}-8q^{4}-\beta _{2}q^{6}+\cdots\)
550.5.d.d	$550$	$5$	550.d	11.b	$2$	$16$	$16$	$56.853$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			550.5.d.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(1+\beta _{1})q^{3}-8q^{4}+\beta _{2}q^{6}+\cdots\)
550.5.d.e	$550$	$5$	550.d	11.b	$2$	$24$	$24$	$56.853$		None			✓		110.5.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(550, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)