Space of modular forms of level 368, weight 2, and Character 368.w

• Label: 368.2.w
• Level: $368$
• Weight: $2$
• Character orbit: 368.w
• Rep. character: $\chi_{368}(13,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $920$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.w (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 368 \)
Character field:			\(\Q(\zeta_{44})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

	Total	New	Old
Modular forms	1000	1000	0
Cusp forms	920	920	0
Eisenstein series	80	80	0

Trace form

920 * q - 18 * q^2 - 18 * q^3 - 22 * q^4 - 18 * q^5 - 24 * q^6 - 18 * q^8 - 10 * q^10 - 26 * q^11 - 24 * q^12 - 18 * q^13 - 30 * q^14 - 52 * q^15 - 6 * q^16 - 36 * q^17 - 6 * q^18 - 34 * q^19 - 18 * q^20 - 30 * q^21 - 36 * q^22 - 32 * q^24 + 2 * q^26 - 18 * q^27 - 14 * q^28 - 34 * q^29 - 10 * q^30 - 36 * q^31 - 38 * q^32 - 36 * q^33 - 6 * q^34 - 38 * q^35 - 60 * q^36 - 34 * q^37 - 108 * q^38 - 6 * q^40 + 178 * q^42 - 10 * q^43 - 14 * q^44 - 48 * q^45 - 210 * q^46 - 80 * q^47 - 38 * q^48 + 32 * q^49 + 132 * q^50 + 10 * q^51 - 22 * q^52 - 2 * q^53 - 186 * q^54 + 22 * q^56 + 122 * q^58 - 30 * q^59 - 2 * q^60 + 14 * q^61 - 16 * q^62 - 52 * q^63 - 64 * q^64 - 36 * q^65 - 50 * q^66 + 22 * q^67 - 72 * q^68 - 10 * q^69 - 32 * q^70 - 108 * q^72 - 46 * q^74 - 10 * q^75 + 14 * q^76 - 118 * q^77 - 72 * q^78 - 44 * q^79 + 22 * q^80 + 24 * q^81 + 36 * q^82 - 58 * q^83 - 94 * q^84 - 30 * q^85 + 34 * q^86 - 38 * q^88 - 82 * q^90 - 68 * q^91 + 2 * q^92 + 212 * q^93 - 86 * q^94 - 36 * q^95 + 90 * q^96 - 36 * q^97 - 6 * q^98 - 82 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
368.2.w.a	$368$	$2$	368.w	368.w	$44$	$920$	$46$	$2.938$		None		✓	✓	✓	368.2.w.a	$4$	$0$	\(-18\)	\(-18\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{44}]$