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

• Label: 100.3.d
• Level: $100$
• Weight: $3$
• Character orbit: 100.d
• Rep. character: $\chi_{100}(99,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(45\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	36	20	16
Cusp forms	24	16	8
Eisenstein series	12	4	8

Trace form

\( 16 q - 2 q^{4} + 18 q^{6} + 40 q^{9} + O(q^{10}) \)

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.d.a	$100$	$3$	100.d	20.d	$2$	$8$	$8$	$2.725$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
100.3.d.b	$100$	$3$	100.d	20.d	$2$	$8$	$8$	$2.725$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{20}q^{2}+\zeta_{20}^{6}q^{3}+(1+\zeta_{20}^{4})q^{4}+\cdots\)

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

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