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

• Label: 936.2.ed
• Level: $936$
• Weight: $2$
• Character orbit: 936.ed
• Rep. character: $\chi_{936}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $272$
• Newform subspaces: $6$
• Sturm bound: $336$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(336\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	704	288	416
Cusp forms	640	272	368
Eisenstein series	64	16	48

Trace form

\( 272 q + 4 q^{2} - 6 q^{4} + 10 q^{8} + O(q^{10}) \)

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.ed.a	$936$	$2$	936.ed	104.u	$12$	$4$	$1$	$7.474$	\(\Q(\zeta_{12})\)	None					312.2.bt.a	$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots\)
936.2.ed.b	$936$	$2$	936.ed	104.u	$12$	$4$	$1$	$7.474$	\(\Q(\zeta_{12})\)	None					312.2.bt.a	$2$	$0$	\(4\)	\(0\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}^{3})q^{2}-2\zeta_{12}^{3}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
936.2.ed.c	$936$	$2$	936.ed	104.u	$12$	$48$	$12$	$7.474$		None					312.2.bt.c	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
936.2.ed.d	$936$	$2$	936.ed	104.u	$12$	$48$	$12$	$7.474$		None					104.2.u.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
936.2.ed.e	$936$	$2$	936.ed	104.u	$12$	$56$	$14$	$7.474$		None					312.2.bt.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
936.2.ed.f	$936$	$2$	936.ed	104.u	$12$	$112$	$28$	$7.474$		None		✓	✓		936.2.ed.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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