Space of modular forms of level 108, weight 4, and Character 108.l

• Label: 108.4.l
• Level: $108$
• Weight: $4$
• Character orbit: 108.l
• Rep. character: $\chi_{108}(11,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $312$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 108 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).

	Total	New	Old
Modular forms	336	336	0
Cusp forms	312	312	0
Eisenstein series	24	24	0

Trace form

312 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 123 * q^12 - 12 * q^13 + 69 * q^14 - 6 * q^16 - 18 * q^17 + 351 * q^18 + 225 * q^20 - 12 * q^21 - 6 * q^22 - 300 * q^24 - 12 * q^25 - 12 * q^28 - 96 * q^29 - 207 * q^30 - 696 * q^32 + 858 * q^33 - 30 * q^34 - 1056 * q^36 - 6 * q^37 - 900 * q^38 - 381 * q^40 + 138 * q^41 + 2574 * q^42 + 2655 * q^44 - 672 * q^45 - 3 * q^46 - 435 * q^48 - 12 * q^49 - 2829 * q^50 + 1371 * q^52 - 4458 * q^54 - 2925 * q^56 + 660 * q^57 + 885 * q^58 + 966 * q^60 - 12 * q^61 + 1872 * q^62 - 3 * q^64 - 708 * q^65 + 3093 * q^66 + 2211 * q^68 - 1572 * q^69 - 1011 * q^70 - 4524 * q^72 - 6 * q^73 - 5883 * q^74 - 198 * q^76 - 996 * q^77 - 2976 * q^78 + 444 * q^81 - 12 * q^82 + 6324 * q^84 - 762 * q^85 + 8322 * q^86 + 1530 * q^88 + 4212 * q^89 - 1104 * q^90 - 3255 * q^92 + 7404 * q^93 + 2019 * q^94 + 582 * q^96 - 66 * q^97 + 2898 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.4.l.a	$108$	$4$	108.l	108.l	$18$	$312$	$52$	$6.372$		None		✓	✓	✓	108.4.l.a	$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$