Space of modular forms of level 99, weight 3, and Character 99.h

• Label: 99.3.h
• Level: $99$
• Weight: $3$
• Character orbit: 99.h
• Rep. character: $\chi_{99}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(99, [\chi])\).

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

\( 44 q - q^{3} + 38 q^{4} + q^{5} - 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.3.h.a	$99$	$3$	99.h	99.h	$6$	$4$	$2$	$2.698$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(5\)	\(-1\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2\beta _{2}-\beta _{3})q^{3}-4\beta _{2}q^{4}+(3-6\beta _{1}+\cdots)q^{5}+\cdots\)
99.3.h.b	$99$	$3$	99.h	99.h	$6$	$40$	$20$	$2.698$		None		$4$	$0$	\(0\)	\(-6\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$