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

• Label: 936.2.g
• Level: $936$
• Weight: $2$
• Character orbit: 936.g
• Rep. character: $\chi_{936}(469,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $6$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	176	60	116
Cusp forms	160	60	100
Eisenstein series	16	0	16

Trace form

\( 60 q - 2 q^{2} + 6 q^{4} - 4 q^{7} + 4 q^{8} + O(q^{10}) \)

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	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.g.a	$936$	$2$	936.g	8.b	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None					104.2.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}+2 i q^{4}+3 i q^{5}+3 q^{7}+\cdots\)
936.2.g.b	$936$	$2$	936.g	8.b	$2$	$4$	$4$	$7.474$	\(\Q(\zeta_{12})\)	None					104.2.b.b	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}-\beta_1)q^{2}+(\beta_{3}+\beta_1)q^{4}+(-2\beta_{3}+2\beta_1-2)q^{5}+\cdots\)
936.2.g.c	$936$	$2$	936.g	8.b	$2$	$6$	$6$	$7.474$	6.0.399424.1	None					104.2.b.c	$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{5})q^{4}-\beta _{1}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
936.2.g.d	$936$	$2$	936.g	8.b	$2$	$8$	$8$	$7.474$	\(\Q(\zeta_{20})\)	None					312.2.g.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{6} q^{2}-\beta_1 q^{4}+(\beta_{6}-\beta_{5}-\beta_{3}+\cdots+1)q^{5}+\cdots\)
936.2.g.e	$936$	$2$	936.g	8.b	$2$	$16$	$16$	$7.474$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					312.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{2}-\beta _{2}q^{4}-\beta _{14}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
936.2.g.f	$936$	$2$	936.g	8.b	$2$	$24$	$24$	$7.474$		None		✓	✓		936.2.g.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)