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

• Label: 100.4.c
• Level: $100$
• Weight: $4$
• Character orbit: 100.c
• Rep. character: $\chi_{100}(49,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	54	4	50
Cusp forms	36	4	32
Eisenstein series	18	0	18

Trace form

\( 4 q + 74 q^{9} + O(q^{10}) \)

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.c.a	$100$	$4$	100.c	5.b	$2$	$2$	$2$	$5.900$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+8iq^{7}+11q^{9}-60q^{11}+\cdots\)
100.4.c.b	$100$	$4$	100.c	5.b	$2$	$2$	$2$	$5.900$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-26iq^{7}+26q^{9}+45q^{11}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)