Space of modular forms of level 100, weight 6, and Character 100.c

• Label: 100.6.c
• Level: $100$
• Weight: $6$
• Character orbit: 100.c
• Rep. character: $\chi_{100}(49,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $90$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	100.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(90\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(100, [\chi])\).

	Total	New	Old
Modular forms	84	8	76
Cusp forms	66	8	58
Eisenstein series	18	0	18

Trace form

\( 8 q - 1348 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.6.c.a	$100$	$6$	100.c	5.b	$2$	$2$	$2$	$16.038$	\(\Q(\sqrt{-1}) \)	None					20.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+11iq^{3}-109iq^{7}-241q^{9}-480q^{11}+\cdots\)
100.6.c.b	$100$	$6$	100.c	5.b	$2$	$2$	$2$	$16.038$	\(\Q(\sqrt{-1}) \)	None					4.6.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+6iq^{3}-44iq^{7}+99q^{9}+540q^{11}+\cdots\)
100.6.c.c	$100$	$6$	100.c	5.b	$2$	$4$	$4$	$16.038$	\(\Q(i, \sqrt{409})\)	None		✓	✓		100.6.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+2\beta _{2})q^{3}+(-6\beta _{1}+4\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

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