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

• Label: 100.4.g
• Level: $100$
• Weight: $4$
• Character orbit: 100.g
• Rep. character: $\chi_{100}(21,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	192	28	164
Cusp forms	168	28	140
Eisenstein series	24	0	24

Trace form

\( 28 q - 4 q^{3} - 25 q^{5} + 16 q^{7} - 13 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.4.g.a	$100$	$4$	100.g	25.d	$5$	$28$	$7$	$5.900$		None		$2$	$0$	\(0\)	\(-4\)	\(-25\)	\(16\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)