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}$