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

• Label: 403.2.bz
• Level: $403$
• Weight: $2$
• Character orbit: 403.bz
• Rep. character: $\chi_{403}(38,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $288$
• Newform subspaces: $1$
• Sturm bound: $74$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bz (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 403 \)
Character field:			\(\Q(\zeta_{30})\)
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	320	320	0
Cusp forms	288	288	0
Eisenstein series	32	32	0

Trace form

288 * q - 16 * q^3 + 60 * q^4 + 16 * q^9 - 42 * q^10 - 58 * q^12 - 7 * q^13 - 26 * q^14 - 84 * q^16 - 30 * q^17 + 44 * q^22 + 44 * q^23 + 124 * q^25 - 21 * q^26 + 2 * q^27 - 44 * q^29 - 204 * q^30 - 34 * q^35 + 134 * q^36 + 38 * q^38 - 11 * q^39 - 84 * q^40 - 64 * q^42 + 60 * q^43 - 42 * q^48 - 50 * q^49 + 14 * q^51 - 13 * q^52 - 12 * q^53 - 92 * q^55 - 56 * q^56 + 52 * q^61 + 18 * q^62 + 174 * q^64 - 46 * q^65 - 128 * q^66 - 140 * q^68 - 226 * q^69 + 82 * q^74 + 46 * q^75 + 144 * q^77 - 95 * q^78 + 30 * q^79 + 104 * q^81 - 2 * q^82 + 30 * q^87 + 52 * q^88 - 328 * q^90 + 78 * q^91 + 152 * q^92 - 60 * q^94 - 150 * q^95

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.bz.a	$403$	$2$	403.bz	403.az	$30$	$288$	$36$	$3.218$		None		✓	✓	✓	403.2.bz.a	$4$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$