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

• Label: 936.2.m
• Level: $936$
• Weight: $2$
• Character orbit: 936.m
• Rep. character: $\chi_{936}(181,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $9$
• 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.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)
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	72	104
Cusp forms	160	68	92
Eisenstein series	16	4	12

Trace form

\( 68 q - 2 q^{4} + O(q^{10}) \)

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.m.a	$936$	$2$	936.m	104.e	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None					312.2.m.a	$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-2 i q^{4}-2 q^{5}+(2 i+2)q^{8}+\cdots\)
936.2.m.b	$936$	$2$	936.m	104.e	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None					104.2.e.a	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-2 i q^{4}+q^{5}+3 i q^{7}+\cdots\)
936.2.m.c	$936$	$2$	936.m	104.e	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None					104.2.e.a	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+1)q^{2}-2 i q^{4}-q^{5}-3 i q^{7}+\cdots\)
936.2.m.d	$936$	$2$	936.m	104.e	$2$	$2$	$2$	$7.474$	\(\Q(\sqrt{-1}) \)	None					312.2.m.a	$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+1)q^{2}-2 i q^{4}+2 q^{5}+(-2 i-2)q^{8}+\cdots\)
936.2.m.e	$936$	$2$	936.m	104.e	$2$	$4$	$4$	$7.474$	\(\Q(\sqrt{-2}, \sqrt{13})\)	\(\Q(\sqrt{-78}) \)		✓			936.2.m.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}-2\beta _{2}q^{8}-\beta _{3}q^{13}+\cdots\)
936.2.m.f	$936$	$2$	936.m	104.e	$2$	$8$	$8$	$7.474$	8.0.4521217600.1	None					104.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{6}q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
936.2.m.g	$936$	$2$	936.m	104.e	$2$	$8$	$8$	$7.474$	8.0.\(\cdots\).21	\(\Q(\sqrt{-39}) \)		✓			936.2.m.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{5}q^{2}+(-\beta _{2}-\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
936.2.m.h	$936$	$2$	936.m	104.e	$2$	$16$	$16$	$7.474$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			936.2.m.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{2}+\beta _{3}q^{4}+\beta _{14}q^{5}-\beta _{5}q^{7}+\cdots\)
936.2.m.i	$936$	$2$	936.m	104.e	$2$	$24$	$24$	$7.474$		None			✓		312.2.m.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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