Space of modular forms of level 100, weight 2, and Character 100.l

• Label: 100.2.l
• Level: $100$
• Weight: $2$
• Character orbit: 100.l
• Rep. character: $\chi_{100}(3,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $104$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).

	Total	New	Old
Modular forms	136	136	0
Cusp forms	104	104	0
Eisenstein series	32	32	0

Trace form

104 * q - 8 * q^2 - 10 * q^4 - 16 * q^5 - 6 * q^6 - 14 * q^8 - 20 * q^9 - 16 * q^10 - 10 * q^12 - 18 * q^13 - 10 * q^14 - 6 * q^16 - 26 * q^17 - 4 * q^18 - 6 * q^20 - 12 * q^21 - 10 * q^22 - 26 * q^25 - 16 * q^26 - 10 * q^28 - 20 * q^29 - 10 * q^30 - 18 * q^32 - 20 * q^33 - 10 * q^34 - 22 * q^36 - 6 * q^37 + 20 * q^38 + 44 * q^40 - 12 * q^41 + 90 * q^42 + 60 * q^44 - 26 * q^45 - 6 * q^46 + 120 * q^48 + 94 * q^50 + 84 * q^52 - 38 * q^53 + 120 * q^54 - 6 * q^56 - 20 * q^57 + 52 * q^58 + 90 * q^60 - 12 * q^61 + 40 * q^62 + 20 * q^64 - 22 * q^65 - 30 * q^66 + 2 * q^68 - 20 * q^69 - 10 * q^70 - 28 * q^72 + 2 * q^73 - 20 * q^77 + 20 * q^78 - 26 * q^80 - 18 * q^81 - 66 * q^82 - 90 * q^84 + 48 * q^85 - 6 * q^86 - 130 * q^88 + 110 * q^89 - 166 * q^90 - 110 * q^92 + 60 * q^93 - 170 * q^94 + 14 * q^96 + 154 * q^97 - 144 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.2.l.a	$100$	$2$	100.l	100.l	$20$	$8$	$1$	$0.799$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		✓			100.2.l.a	$4$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
100.2.l.b	$100$	$2$	100.l	100.l	$20$	$96$	$12$	$0.799$		None		✓	✓		100.2.l.b	$4$	$0$	\(-10\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$