Space of modular forms of level 100, weight 10, and Character 100.c

• Label: 100.10.c
• Level: $100$
• Weight: $10$
• Character orbit: 100.c
• Rep. character: $\chi_{100}(49,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $4$
• Sturm bound: $150$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	100.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(150\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(100, [\chi])\).

	Total	New	Old
Modular forms	144	14	130
Cusp forms	126	14	112
Eisenstein series	18	0	18

Trace form

\( 14 q - 93004 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(100, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.10.c.a	$100$	$10$	100.c	5.b	$2$	$2$	$2$	$51.504$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+114iq^{3}+3164iq^{7}-32301q^{9}+\cdots\)
100.10.c.b	$100$	$10$	100.c	5.b	$2$	$2$	$2$	$51.504$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+24iq^{3}-266iq^{7}+17379q^{9}+\cdots\)
100.10.c.c	$100$	$10$	100.c	5.b	$2$	$4$	$4$	$51.504$	\(\Q(i, \sqrt{79})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-13\beta _{1}+\beta _{3})q^{3}+(19\beta _{1}-69\beta _{3})q^{7}+\cdots\)
100.10.c.d	$100$	$10$	100.c	5.b	$2$	$6$	$6$	$51.504$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(4\beta _{1}+5\beta _{2}+\beta _{5})q^{7}+(1101+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)