Space of modular forms of level 936, weight 2, and Character 936.c

• Label: 936.2.c
• Level: $936$
• Weight: $2$
• Character orbit: 936.c
• Rep. character: $\chi_{936}(649,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(936, [\chi])\).

	Total	New	Old
Modular forms	184	18	166
Cusp forms	152	18	134
Eisenstein series	32	0	32

Trace form

\( 18 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(936, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
936.2.c.a	$936$	$2$	936.c	13.b	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-iq^{7}+2iq^{11}+(-3+i)q^{13}+\cdots\)
936.2.c.b	$936$	$2$	936.c	13.b	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{7}+iq^{11}+(3-i)q^{13}-2q^{17}+\cdots\)
936.2.c.c	$936$	$2$	936.c	13.b	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+iq^{7}+iq^{11}+(3-i)q^{13}+\cdots\)
936.2.c.d	$936$	$2$	936.c	13.b	$2$	$4$	$4$	$7.474$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
936.2.c.e	$936$	$2$	936.c	13.b	$2$	$8$	$8$	$7.474$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{4})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(936, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(936, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)