Space of modular forms of level 416, weight 2, and Character 416.bz

• Label: 416.2.bz
• Level: $416$
• Weight: $2$
• Character orbit: 416.bz
• Rep. character: $\chi_{416}(69,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $432$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bz (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 416 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(416, [\chi])\).

	Total	New	Old
Modular forms	464	464	0
Cusp forms	432	432	0
Eisenstein series	32	32	0

Trace form

432 * q - 12 * q^2 - 4 * q^3 - 4 * q^4 - 12 * q^6 - 12 * q^7 - 4 * q^9 - 4 * q^10 - 12 * q^11 - 48 * q^12 - 8 * q^13 - 48 * q^14 - 4 * q^16 - 12 * q^19 + 36 * q^20 - 20 * q^22 - 4 * q^23 - 12 * q^24 - 16 * q^25 + 32 * q^26 + 32 * q^27 - 72 * q^28 - 4 * q^29 + 12 * q^30 + 48 * q^32 - 24 * q^33 - 4 * q^35 + 8 * q^36 - 12 * q^37 + 24 * q^38 - 56 * q^39 - 56 * q^40 - 12 * q^41 - 44 * q^42 - 4 * q^43 - 12 * q^45 - 12 * q^46 - 56 * q^48 - 12 * q^50 - 40 * q^51 - 96 * q^52 - 16 * q^53 - 12 * q^54 + 28 * q^55 + 36 * q^56 - 12 * q^58 + 84 * q^59 - 4 * q^61 - 8 * q^62 - 24 * q^63 - 16 * q^64 - 16 * q^65 - 160 * q^66 - 12 * q^67 - 12 * q^68 - 4 * q^69 - 12 * q^71 + 96 * q^72 - 4 * q^74 - 56 * q^75 - 12 * q^76 - 16 * q^77 + 132 * q^78 - 12 * q^80 + 76 * q^82 - 12 * q^84 - 72 * q^85 - 4 * q^87 + 36 * q^88 - 12 * q^89 - 112 * q^90 - 56 * q^91 - 160 * q^92 + 24 * q^93 + 12 * q^94 - 136 * q^95 - 24 * q^97 - 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(416, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
416.2.bz.a	$416$	$2$	416.bz	416.az	$24$	$432$	$54$	$3.322$		None		✓	✓	✓	416.2.bz.a	$4$	$0$	\(-12\)	\(-4\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{24}]$