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

• Label: 550.2.g
• Level: $550$
• Weight: $2$
• Character orbit: 550.g
• Rep. character: $\chi_{550}(291,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $120$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
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	120	256
Cusp forms	344	120	224
Eisenstein series	32	0	32

Trace form

120 * q - 4 * q^3 - 30 * q^4 - 6 * q^5 - 4 * q^6 - 6 * q^7 - 34 * q^9 - 4 * q^10 - 4 * q^11 + 6 * q^12 + 24 * q^13 - 6 * q^15 - 30 * q^16 + 2 * q^17 - 6 * q^20 - 8 * q^21 - 2 * q^22 - 2 * q^23 - 4 * q^24 + 14 * q^27 + 24 * q^28 - 12 * q^29 + 10 * q^30 + 36 * q^33 + 10 * q^35 - 24 * q^36 - 52 * q^37 - 24 * q^38 + 10 * q^39 - 4 * q^40 + 40 * q^41 + 60 * q^42 + 44 * q^43 - 4 * q^44 - 78 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 68 * q^49 + 36 * q^50 - 8 * q^51 - 16 * q^52 + 72 * q^53 - 10 * q^54 - 54 * q^55 + 60 * q^57 + 48 * q^58 + 2 * q^59 + 4 * q^60 - 42 * q^61 + 10 * q^62 + 68 * q^63 - 30 * q^64 + 6 * q^65 - 16 * q^66 - 58 * q^67 - 8 * q^68 - 30 * q^69 + 2 * q^70 - 68 * q^71 + 188 * q^73 - 20 * q^74 + 40 * q^75 + 40 * q^76 + 4 * q^77 - 34 * q^78 - 32 * q^79 + 14 * q^80 - 16 * q^81 - 12 * q^82 - 2 * q^83 - 8 * q^84 - 10 * q^85 - 24 * q^86 + 112 * q^87 + 8 * q^88 - 10 * q^89 - 52 * q^90 - 40 * q^91 + 8 * q^92 + 48 * q^93 - 16 * q^94 - 30 * q^95 - 4 * q^96 + 44 * q^97 - 32 * q^98 - 72 * 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.g.a	$550$	$2$	550.g	275.g	$5$	$12$	$3$	$4.392$	12.0.\(\cdots\).1	None		✓			550.2.g.a	$2$	$0$	\(3\)	\(-2\)	\(-5\)	\(-7\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{8}q^{2}+(\beta _{5}-\beta _{8}-\beta _{10})q^{3}-\beta _{6}q^{4}+\cdots\)
550.2.g.b	$550$	$2$	550.g	275.g	$5$	$48$	$12$	$4.392$		None		✓			550.2.g.b	$2$	$0$	\(12\)	\(2\)	\(-1\)	\(4\)		$\mathrm{SU}(2)[C_{5}]$
550.2.g.c	$550$	$2$	550.g	275.g	$5$	$60$	$15$	$4.392$		None		✓	✓		550.2.g.c	$2$	$0$	\(-15\)	\(-4\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{5}]$

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

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