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

• Label: 403.2.bl
• Level: $403$
• Weight: $2$
• Character orbit: 403.bl
• Rep. character: $\chi_{403}(16,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $288$
• Newform subspaces: $2$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	320	320	0
Cusp forms	288	288	0
Eisenstein series	32	32	0

Trace form

288 * q - 3 * q^2 - 5 * q^3 + 33 * q^4 - 32 * q^5 - 10 * q^6 - 5 * q^7 - 2 * q^8 + 31 * q^9 - 9 * q^10 - 6 * q^11 + 14 * q^12 - 5 * q^13 - 48 * q^14 - 12 * q^15 + 45 * q^16 - 3 * q^17 + 6 * q^18 - q^19 + 15 * q^20 + 38 * q^21 - 34 * q^22 - 18 * q^23 + 43 * q^24 + 232 * q^25 - 6 * q^26 - 68 * q^27 + 3 * q^28 - 23 * q^29 - 36 * q^30 - 60 * q^31 - 26 * q^32 - 25 * q^33 - 136 * q^34 - 28 * q^35 - 152 * q^36 - 26 * q^37 + 16 * q^38 + 18 * q^39 - 116 * q^40 + 13 * q^41 + 31 * q^42 - 28 * q^43 + 12 * q^44 - 52 * q^45 - 15 * q^46 - 20 * q^47 - 11 * q^48 + 45 * q^49 - 21 * q^50 - 104 * q^51 + 62 * q^52 + 16 * q^53 + 49 * q^54 - 40 * q^55 - 78 * q^56 + 140 * q^57 + 31 * q^58 - 19 * q^59 - 52 * q^60 + 34 * q^61 + 3 * q^62 - 122 * q^63 - 102 * q^64 + 17 * q^65 + 16 * q^66 + 6 * q^67 + 86 * q^68 - 67 * q^69 - 22 * q^70 + 41 * q^71 + 47 * q^72 - 56 * q^73 - 9 * q^74 - 4 * q^75 - 34 * q^76 + 40 * q^77 - 72 * q^78 + 80 * q^79 - 114 * q^80 - 29 * q^81 + 45 * q^82 - 134 * q^83 + 81 * q^84 - 54 * q^85 + 212 * q^86 - 38 * q^87 + 82 * q^88 + 21 * q^89 - 26 * q^90 + 46 * q^91 - 336 * q^92 - 30 * q^93 - 18 * q^94 + 34 * q^95 + 186 * q^96 + 13 * q^97 + 88 * q^98 - 60 * 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.bl.a	$403$	$2$	403.bl	403.al	$15$	$8$	$1$	$3.218$	\(\Q(\zeta_{15})\)	None		✓			403.2.bl.a	$4$	$1$	\(-4\)	\(-5\)	\(-24\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+2\zeta_{15}^{4}+\cdots)q^{2}+\cdots\)
403.2.bl.b	$403$	$2$	403.bl	403.al	$15$	$280$	$35$	$3.218$		None		✓	✓		403.2.bl.b	$4$	$0$	\(1\)	\(0\)	\(-8\)	\(-2\)		$\mathrm{SU}(2)[C_{15}]$