Space of modular forms of level 36, weight 2, and Character 36.h

• Label: 36.2.h
• Level: $36$
• Weight: $2$
• Character orbit: 36.h
• Rep. character: $\chi_{36}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

Trace form

8 * q - 3 * q^2 - q^4 - 6 * q^5 - 3 * q^6 - 6 * q^9 - 8 * q^10 + 6 * q^12 - 2 * q^13 + 12 * q^14 - q^16 + 18 * q^18 + 18 * q^20 - 6 * q^21 + 3 * q^22 + 3 * q^24 - 6 * q^25 - 12 * q^28 + 6 * q^29 - 18 * q^30 - 33 * q^32 + 24 * q^33 + 7 * q^34 - 33 * q^36 - 8 * q^37 - 27 * q^38 + 10 * q^40 + 24 * q^41 - 18 * q^42 + 6 * q^45 + 12 * q^46 + 21 * q^48 - 10 * q^49 + 21 * q^50 + 16 * q^52 + 39 * q^54 + 18 * q^56 + 6 * q^57 + 4 * q^58 + 6 * q^60 - 2 * q^61 + 26 * q^64 - 30 * q^65 - 24 * q^66 - 15 * q^68 - 30 * q^69 - 6 * q^70 - 21 * q^72 + 4 * q^73 - 30 * q^74 - 3 * q^76 - 30 * q^77 - 12 * q^78 - 30 * q^81 + 10 * q^82 + 30 * q^84 + 8 * q^85 + 21 * q^86 - 21 * q^88 + 6 * q^90 + 24 * q^92 + 30 * q^93 - 18 * q^94 + 12 * q^96 + 4 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
36.2.h.a	$36$	$2$	36.h	36.h	$6$	$8$	$4$	$0.287$	8.0.170772624.1	None		✓	✓	✓	36.2.h.a	$4$	$0$	\(-3\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)