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

\( 104 q - 8 q^{2} - 10 q^{4} - 16 q^{5} - 6 q^{6} - 14 q^{8} - 20 q^{9} + O(q^{10}) \)

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	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	$20$	$8$	$1$	$0.799$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{20}]$	\(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
100.2.l.b	$100$	$2$	100.l	100.l	$20$	$96$	$12$	$0.799$		None		$4$	$0$	\(-10\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$