Space of modular forms of level 403, weight 2, and Character 403.bk

• Label: 403.2.bk
• Level: $403$
• Weight: $2$
• Character orbit: 403.bk
• Rep. character: $\chi_{403}(9,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $280$
• Newform subspaces: $1$
• Sturm bound: $74$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bk (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 403 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(74\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

	Total	New	Old
Modular forms	312	312	0
Cusp forms	280	280	0
Eisenstein series	32	32	0

Trace form

280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
403.2.bk.a	$403$	$2$	403.bk	403.ak	$15$	$280$	$35$	$3.218$		None		✓	✓	✓	403.2.bj.a	$2$	$0$	\(-3\)	\(-9\)	\(-8\)	\(-13\)		$\mathrm{SU}(2)[C_{15}]$