Space of modular forms of level 100, weight 4, and Character 100.l

• Label: 100.4.l
• Level: $100$
• Weight: $4$
• Character orbit: 100.l
• Rep. character: $\chi_{100}(3,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $344$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(100, [\chi])\).

	Total	New	Old
Modular forms	376	376	0
Cusp forms	344	344	0
Eisenstein series	32	32	0

Trace form

344 * q - 8 * q^2 - 10 * q^4 - 16 * q^5 - 6 * q^6 + 34 * q^8 - 20 * q^9 + 64 * q^10 + 70 * q^12 - 62 * q^13 - 10 * q^14 - 6 * q^16 + 114 * q^17 - 316 * q^18 - 326 * q^20 - 12 * q^21 - 370 * q^22 - 126 * q^25 - 16 * q^26 + 870 * q^28 - 20 * q^29 + 1230 * q^30 + 622 * q^32 - 100 * q^33 - 10 * q^34 - 262 * q^36 - 346 * q^37 + 880 * q^38 + 204 * q^40 - 12 * q^41 - 470 * q^42 - 1340 * q^44 - 606 * q^45 - 6 * q^46 - 3400 * q^48 - 2206 * q^50 - 2356 * q^52 + 678 * q^53 - 3780 * q^54 - 6 * q^56 + 940 * q^57 - 1112 * q^58 + 2810 * q^60 - 12 * q^61 + 2900 * q^62 + 4820 * q^64 + 1758 * q^65 - 870 * q^66 + 2418 * q^68 - 20 * q^69 + 3030 * q^70 + 1892 * q^72 - 1962 * q^73 + 240 * q^76 - 3140 * q^77 - 3460 * q^78 - 2106 * q^80 + 4362 * q^81 - 8826 * q^82 - 11290 * q^84 + 3248 * q^85 - 6 * q^86 - 1570 * q^88 + 1410 * q^89 + 3494 * q^90 + 6130 * q^92 - 1300 * q^93 + 11030 * q^94 - 1746 * q^96 - 12626 * q^97 + 13324 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.4.l.a	$100$	$4$	100.l	100.l	$20$	$8$	$1$	$5.900$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		✓			100.4.l.a	$4$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(-2+2\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{2}+\cdots\)
100.4.l.b	$100$	$4$	100.l	100.l	$20$	$336$	$42$	$5.900$		None		✓	✓		100.4.l.b	$4$	$0$	\(-4\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$