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

• Label: 936.2.q
• Level: $936$
• Weight: $2$
• Character orbit: 936.q
• Rep. character: $\chi_{936}(313,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $7$
• Sturm bound: $336$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(336\)
Trace bound:			\(7\)
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	72	280
Cusp forms	320	72	248
Eisenstein series	32	0	32

Trace form

72 * q - 2 * q^3 - 4 * q^5 + 2 * q^9 + 14 * q^11 + 12 * q^15 + 12 * q^17 - 12 * q^19 + 8 * q^21 - 36 * q^25 - 26 * q^27 - 12 * q^29 - 6 * q^33 - 12 * q^35 - 18 * q^41 + 6 * q^43 - 28 * q^45 - 12 * q^47 - 24 * q^49 + 20 * q^51 + 24 * q^53 + 24 * q^55 - 22 * q^57 + 50 * q^59 + 12 * q^61 + 36 * q^63 - 8 * q^65 + 6 * q^67 + 24 * q^69 + 36 * q^73 + 46 * q^75 + 16 * q^77 - 12 * q^79 + 34 * q^81 + 32 * q^83 + 76 * q^87 + 48 * q^89 + 24 * q^93 - 16 * q^95 - 18 * q^97 - 104 * 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.q.a	$936$	$2$	936.q	9.c	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.q.a	$2$	$0$	\(0\)	\(-3\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
936.2.q.b	$936$	$2$	936.q	9.c	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.q.b	$2$	$0$	\(0\)	\(3\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
936.2.q.c	$936$	$2$	936.q	9.c	$3$	$2$	$1$	$7.474$	\(\Q(\sqrt{-3}) \)	None		✓			936.2.q.c	$2$	$0$	\(0\)	\(3\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
936.2.q.d	$936$	$2$	936.q	9.c	$3$	$12$	$6$	$7.474$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			936.2.q.d	$2$	$0$	\(0\)	\(-4\)	\(-1\)	\(2\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{3}+(\beta _{2}-\beta _{11})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
936.2.q.e	$936$	$2$	936.q	9.c	$3$	$16$	$8$	$7.474$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			936.2.q.e	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(-\beta _{5}-\beta _{9}+\beta _{11})q^{5}-\beta _{14}q^{7}+\cdots\)
936.2.q.f	$936$	$2$	936.q	9.c	$3$	$16$	$8$	$7.474$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			936.2.q.f	$2$	$0$	\(0\)	\(0\)	\(1\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{11})q^{5}-\beta _{5}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
936.2.q.g	$936$	$2$	936.q	9.c	$3$	$22$	$11$	$7.474$		None		✓	✓		936.2.q.g	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-4\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)