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

• Label: 936.2.s
• Level: $936$
• Weight: $2$
• Character orbit: 936.s
• Rep. character: $\chi_{936}(529,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $84$
• Newform subspaces: $6$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.s (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	352	84	268
Cusp forms	320	84	236
Eisenstein series	32	0	32

Trace form

84 * q + 8 * q^15 + 8 * q^17 - 16 * q^21 - 8 * q^23 - 42 * q^25 + 6 * q^27 + 12 * q^29 + 6 * q^31 + 2 * q^33 - 30 * q^35 - 20 * q^39 - 12 * q^43 + 12 * q^45 + 6 * q^47 + 84 * q^49 + 18 * q^51 - 32 * q^53 + 24 * q^57 + 24 * q^63 + 6 * q^65 + 32 * q^69 - 4 * q^71 - 4 * q^75 + 4 * q^77 + 20 * q^81 - 20 * q^83 - 12 * q^85 + 10 * q^87 + 6 * q^89 - 6 * q^91 - 14 * q^93 - 8 * q^95 - 48 * q^97 + 32 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
936.2.s.a	$936$	$2$	936.s	117.f	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.r.b	$2$	$1$	\(0\)	\(-3\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\zeta_{6})q^{3}-3\zeta_{6}q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
936.2.s.b	$936$	$2$	936.s	117.f	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.r.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}-3q^{9}+\cdots\)
936.2.s.c	$936$	$2$	936.s	117.f	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.r.c	$2$	$0$	\(0\)	\(3\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+3q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
936.2.s.d	$936$	$2$	936.s	117.f	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.r.d	$2$	$0$	\(0\)	\(3\)	\(1\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+5q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
936.2.s.e	$936$	$2$	936.s	117.f	$3$	$36$	$18$	$7.474$		None		✓			936.2.r.e	$2$	$0$	\(0\)	\(0\)	\(5\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$
936.2.s.f	$936$	$2$	936.s	117.f	$3$	$40$	$20$	$7.474$		None		✓	✓		936.2.r.f	$2$	$0$	\(0\)	\(-3\)	\(1\)	\(-14\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)