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

• Label: 100.3.h
• Level: $100$
• Weight: $3$
• Character orbit: 100.h
• Rep. character: $\chi_{100}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $112$
• 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.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 100 \)
Character field:			\(\Q(\zeta_{10})\)
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	128	128	0
Cusp forms	112	112	0
Eisenstein series	16	16	0

Trace form

\( 112 q - 5 q^{2} - 3 q^{4} - 6 q^{5} + 5 q^{6} + 10 q^{8} - 78 q^{9} + O(q^{10}) \)

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.h.a	$100$	$3$	100.h	100.h	$10$	$8$	$2$	$2.725$	\(\Q(\zeta_{20})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{10}]$	\(q+\zeta_{20}q^{2}+4\zeta_{20}^{2}q^{4}+(-3+3\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
100.3.h.b	$100$	$3$	100.h	100.h	$10$	$104$	$26$	$2.725$		None		$4$	$0$	\(-5\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$