Space of modular forms of level 100, weight 3, and Character 100.f

• Label: 100.3.f
• Level: $100$
• Weight: $3$
• Character orbit: 100.f
• Rep. character: $\chi_{100}(57,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	100.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(100, [\chi])\).

	Total	New	Old
Modular forms	78	6	72
Cusp forms	42	6	36
Eisenstein series	36	0	36

Trace form

\( 6 q - 2 q^{3} + 14 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(100, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.3.f.a	$100$	$3$	100.f	5.c	$4$	$2$	$1$	$2.725$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(7+7i)q^{7}+7iq^{9}+\cdots\)
100.3.f.b	$100$	$3$	100.f	5.c	$4$	$4$	$2$	$2.725$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+3\beta _{1}q^{3}-4\beta _{3}q^{7}+18\beta _{2}q^{9}-15q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

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