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

• Label: 936.2.be
• Level: $936$
• Weight: $2$
• Character orbit: 936.be
• Rep. character: $\chi_{936}(685,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $136$
• Newform subspaces: $3$
• Sturm bound: $336$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.be (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(336\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	352	144	208
Cusp forms	320	136	184
Eisenstein series	32	8	24

Trace form

136 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 + 5 * q^10 + 8 * q^14 + 7 * q^16 + 4 * q^17 - 17 * q^20 + 2 * q^22 + 14 * q^23 - 124 * q^25 - 5 * q^26 + 8 * q^28 - 8 * q^31 - 19 * q^32 + 38 * q^34 - 12 * q^38 - 2 * q^40 + 56 * q^44 - 28 * q^46 + 8 * q^47 - 66 * q^49 - 24 * q^50 + 36 * q^52 - 24 * q^55 + 4 * q^56 - 7 * q^58 - 2 * q^62 + 26 * q^64 - 2 * q^65 + 9 * q^68 + 120 * q^70 + 34 * q^71 - 44 * q^73 + 31 * q^74 + 10 * q^76 - 48 * q^79 - 49 * q^80 - 13 * q^82 + 96 * q^86 + 24 * q^88 - 18 * q^89 - 72 * q^92 - 22 * q^94 - 20 * q^95 - 14 * q^97 - 47 * q^98

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.be.a	$936$	$2$	936.be	104.r	$6$	$24$	$12$	$7.474$		None					104.2.r.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$
936.2.be.b	$936$	$2$	936.be	104.r	$6$	$56$	$28$	$7.474$		None		✓			936.2.be.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
936.2.be.c	$936$	$2$	936.be	104.r	$6$	$56$	$28$	$7.474$		None					312.2.bb.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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