Space of modular forms of level 33, weight 2, and Character 33.e

• Label: 33.2.e
• Level: $33$
• Weight: $2$
• Character orbit: 33.e
• Rep. character: $\chi_{33}(4,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(33, [\chi])\).

	Total	New	Old
Modular forms	24	8	16
Cusp forms	8	8	0
Eisenstein series	16	0	16

Trace form

8 * q - 4 * q^2 - 6 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 8 * q^8 - 2 * q^9 + 4 * q^10 - 2 * q^11 - 8 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 10 * q^16 + 14 * q^17 + 6 * q^18 - 20 * q^19 + 6 * q^20 + 16 * q^21 - 4 * q^22 - 12 * q^23 + 12 * q^24 + 10 * q^26 - 12 * q^28 - 4 * q^29 - 4 * q^31 - 48 * q^32 - 10 * q^33 + 8 * q^34 - 6 * q^36 + 6 * q^37 - 10 * q^38 - 16 * q^39 + 4 * q^40 + 20 * q^41 - 10 * q^42 + 16 * q^43 + 34 * q^44 - 4 * q^45 + 10 * q^46 + 14 * q^47 + 8 * q^48 + 4 * q^49 + 18 * q^50 + 10 * q^52 + 10 * q^53 + 8 * q^54 + 16 * q^55 + 12 * q^56 - 24 * q^58 - 26 * q^59 - 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 - 28 * q^65 - 12 * q^66 - 4 * q^67 - 28 * q^68 - 6 * q^69 - 6 * q^70 - 12 * q^71 - 2 * q^72 + 20 * q^73 - 30 * q^74 + 8 * q^75 + 40 * q^76 - 2 * q^77 + 16 * q^78 - 6 * q^79 + 22 * q^80 - 2 * q^81 - 14 * q^82 + 34 * q^83 - 2 * q^85 + 8 * q^86 + 24 * q^87 - 62 * q^88 - 4 * q^89 + 4 * q^90 + 6 * q^91 + 10 * q^92 + 20 * q^93 + 18 * q^94 + 30 * q^95 - 8 * q^96 - 30 * q^97 + 40 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(33, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.2.e.a	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	\(\Q(\zeta_{10})\)	None		✓			33.2.e.a	$2$	$0$	\(-3\)	\(-1\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b	$33$	$2$	33.e	11.c	$5$	$4$	$1$	$0.264$	\(\Q(\zeta_{10})\)	None		✓			33.2.e.b	$2$	$0$	\(-1\)	\(1\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)