Space of modular forms of level 55, weight 2, and Character 55.j

• Label: 55.2.j
• Level: $55$
• Weight: $2$
• Character orbit: 55.j
• Rep. character: $\chi_{55}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(55, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	16	16	0
Eisenstein series	16	16	0

Trace form

16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.2.j.a	$55$	$2$	55.j	55.j	$10$	$16$	$4$	$0.439$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	55.2.j.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots\)