Space of modular forms of level 289, weight 2, and Character 289.f

• Label: 289.2.f
• Level: $289$
• Weight: $2$
• Character orbit: 289.f
• Rep. character: $\chi_{289}(18,\cdot)$
• Character field: $\Q(\zeta_{17})$
• Dimension: $384$
• Newform subspaces: $1$
• Sturm bound: $51$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.f (of order \(17\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 289 \)
Character field:			\(\Q(\zeta_{17})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(51\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(289, [\chi])\).

	Total	New	Old
Modular forms	416	416	0
Cusp forms	384	384	0
Eisenstein series	32	32	0

Trace form

384 * q - 13 * q^2 - 13 * q^3 - 33 * q^4 - 43 * q^5 - 5 * q^6 - 13 * q^7 - 5 * q^8 - 25 * q^9 - 35 * q^10 - 5 * q^11 + 11 * q^12 - 3 * q^13 - 74 * q^14 + 5 * q^15 - 145 * q^16 - q^17 + 15 * q^18 + 5 * q^19 + 23 * q^20 - 40 * q^21 + 19 * q^22 + 3 * q^23 - 42 * q^24 - 113 * q^25 + 19 * q^26 - 28 * q^27 + 43 * q^28 + 7 * q^29 + 45 * q^30 + 11 * q^31 + 41 * q^32 - 26 * q^33 + 35 * q^34 + 35 * q^35 + 37 * q^36 + 23 * q^37 - 152 * q^38 - 29 * q^39 + 62 * q^40 + 31 * q^41 + 65 * q^42 + 17 * q^43 - q^44 - 98 * q^45 - 9 * q^46 + 12 * q^47 - 114 * q^48 + 5 * q^49 + 61 * q^50 - 85 * q^51 - 116 * q^52 + 8 * q^53 - 356 * q^54 + 45 * q^55 + 91 * q^56 + 63 * q^57 - 40 * q^58 + 49 * q^59 + 133 * q^60 + 55 * q^61 - 19 * q^62 + 14 * q^63 + 67 * q^64 + 46 * q^65 - 144 * q^66 - 82 * q^67 + 103 * q^68 - 54 * q^69 + 103 * q^70 - 77 * q^71 + 114 * q^72 + 63 * q^73 - 92 * q^74 - 46 * q^75 - 71 * q^76 - 105 * q^77 + 151 * q^78 - 68 * q^79 - 37 * q^80 - 73 * q^81 + 103 * q^82 - 5 * q^83 + 183 * q^84 - 168 * q^85 + 105 * q^86 + 91 * q^87 - 75 * q^88 + 57 * q^89 + 223 * q^90 + 35 * q^91 - 15 * q^92 + 95 * q^93 - 331 * q^94 + 95 * q^95 - 122 * q^96 + 79 * q^97 - 63 * q^98 + 139 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(289, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
289.2.f.a	$289$	$2$	289.f	289.f	$17$	$384$	$24$	$2.308$		None		✓	✓	✓	289.2.f.a	$2$	$0$	\(-13\)	\(-13\)	\(-43\)	\(-13\)		$\mathrm{SU}(2)[C_{17}]$