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

• Label: 550.2.k
• Level: $550$
• Weight: $2$
• Character orbit: 550.k
• Rep. character: $\chi_{550}(111,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.k (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	376	96	280
Cusp forms	344	96	248
Eisenstein series	32	0	32

Trace form

96 * q + 2 * q^2 + 4 * q^3 - 24 * q^4 - 6 * q^5 + 2 * q^8 - 16 * q^9 + 6 * q^10 + 2 * q^11 - 6 * q^12 + 12 * q^13 + 8 * q^14 - 16 * q^15 - 24 * q^16 + 28 * q^17 - 24 * q^18 - 6 * q^20 + 24 * q^21 - 4 * q^23 - 10 * q^25 - 36 * q^26 - 26 * q^27 - 12 * q^29 + 20 * q^30 + 12 * q^31 - 8 * q^32 + 4 * q^33 - 22 * q^34 + 40 * q^35 - 16 * q^36 - 6 * q^37 + 16 * q^38 - 24 * q^39 + 6 * q^40 + 12 * q^41 + 24 * q^42 - 48 * q^43 + 2 * q^44 + 52 * q^45 - 56 * q^47 - 6 * q^48 + 64 * q^49 + 26 * q^50 + 64 * q^51 + 12 * q^52 - 50 * q^53 + 6 * q^55 + 8 * q^56 + 80 * q^57 + 28 * q^58 - 18 * q^59 + 14 * q^60 + 20 * q^61 - 36 * q^62 + 56 * q^63 - 24 * q^64 - 34 * q^65 + 8 * q^66 - 2 * q^67 - 92 * q^68 - 94 * q^69 - 8 * q^70 - 16 * q^71 + 26 * q^72 - 84 * q^73 + 28 * q^74 - 40 * q^75 + 48 * q^78 - 32 * q^79 + 4 * q^80 - 30 * q^81 - 28 * q^82 - 104 * q^83 - 36 * q^84 + 30 * q^85 + 20 * q^86 - 48 * q^87 + 50 * q^89 - 102 * q^90 - 48 * q^91 - 14 * q^92 + 124 * q^93 + 32 * q^94 + 60 * q^97 + 82 * q^98 - 4 * 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.k.a	$550$	$2$	550.k	25.d	$5$	$4$	$1$	$4.392$	\(\Q(\zeta_{10})\)	None		✓			550.2.k.a	$2$	$0$	\(1\)	\(-6\)	\(5\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)
550.2.k.b	$550$	$2$	550.k	25.d	$5$	$20$	$5$	$4.392$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			550.2.k.b	$2$	$0$	\(-5\)	\(4\)	\(-6\)	\(-16\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{3}q^{2}-\beta _{17}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
550.2.k.c	$550$	$2$	550.k	25.d	$5$	$20$	$5$	$4.392$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			550.2.k.c	$2$	$0$	\(5\)	\(6\)	\(-14\)	\(8\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{6}-\beta _{7}+\beta _{9})q^{2}+(2-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
550.2.k.d	$550$	$2$	550.k	25.d	$5$	$24$	$6$	$4.392$		None		✓			550.2.k.d	$2$	$0$	\(-6\)	\(-2\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$
550.2.k.e	$550$	$2$	550.k	25.d	$5$	$28$	$7$	$4.392$		None		✓	✓		550.2.k.e	$2$	$0$	\(7\)	\(2\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(550, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)