Space of modular forms of level 53, weight 2, and Character 53.d

• Label: 53.2.d
• Level: $53$
• Weight: $2$
• Character orbit: 53.d
• Rep. character: $\chi_{53}(10,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	53.d (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q(\zeta_{13})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(53, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	36	36	0
Eisenstein series	24	24	0

Trace form

36 * q - 8 * q^2 - 9 * q^3 - 6 * q^4 - 5 * q^5 - q^6 - 5 * q^7 - 24 * q^8 - 8 * q^9 - 17 * q^10 + 3 * q^11 + 17 * q^12 + q^13 + 13 * q^14 - 33 * q^15 + 22 * q^16 - 26 * q^17 + 32 * q^18 + q^19 + 19 * q^20 + 9 * q^21 - 13 * q^22 - 12 * q^23 - 53 * q^24 + 26 * q^25 + q^26 + 21 * q^27 + 27 * q^28 + 3 * q^29 + 44 * q^30 - 9 * q^31 + 52 * q^32 - 29 * q^33 + 23 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 91 * q^38 + 31 * q^39 - 36 * q^40 + 20 * q^41 - 18 * q^42 - 37 * q^43 + 19 * q^44 - 28 * q^45 + 31 * q^46 - 18 * q^47 - 35 * q^48 - 12 * q^49 + 13 * q^50 + 7 * q^51 - 140 * q^52 - q^53 - 104 * q^54 + 16 * q^55 - 40 * q^56 - 9 * q^57 - 10 * q^58 - 31 * q^59 - 21 * q^60 - 50 * q^61 + 29 * q^62 + 5 * q^63 + 66 * q^64 - 31 * q^65 - 55 * q^66 + 48 * q^67 + 4 * q^68 + 72 * q^69 + 4 * q^70 + 63 * q^71 + 14 * q^72 + 33 * q^73 + 56 * q^74 - 21 * q^75 + 110 * q^76 + 48 * q^77 + 167 * q^78 - 55 * q^79 + 79 * q^80 + 25 * q^81 + 25 * q^82 + 32 * q^83 - 21 * q^84 + 101 * q^85 + 45 * q^86 + 4 * q^88 - 37 * q^89 + 58 * q^90 - 21 * q^91 - 34 * q^92 - 77 * q^93 - 39 * q^94 + 15 * q^95 - 3 * q^96 - 71 * q^97 - 33 * q^98 + 37 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(53, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
53.2.d.a	$53$	$2$	53.d	53.d	$13$	$36$	$3$	$0.423$		None		✓	✓	✓	53.2.d.a	$2$	$0$	\(-8\)	\(-9\)	\(-5\)	\(-5\)		$\mathrm{SU}(2)[C_{13}]$