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

• Label: 33.2.f
• Level: $33$
• Weight: $2$
• Character orbit: 33.f
• Rep. character: $\chi_{33}(2,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

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

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

Trace form

8 * q - 6 * q^3 - 6 * q^4 - 10 * q^7 + 10 * q^9 + 12 * q^12 - 10 * q^13 - 6 * q^15 + 2 * q^16 + 20 * q^19 + 20 * q^22 - 10 * q^24 + 12 * q^25 - 12 * q^27 - 20 * q^30 - 20 * q^31 - 4 * q^33 - 40 * q^34 - 10 * q^36 - 6 * q^37 + 20 * q^39 + 20 * q^42 + 24 * q^45 + 30 * q^46 + 26 * q^48 + 16 * q^49 + 30 * q^51 + 10 * q^52 - 32 * q^55 - 30 * q^57 + 20 * q^58 + 2 * q^60 - 10 * q^61 - 30 * q^63 - 34 * q^64 - 30 * q^66 - 4 * q^67 - 16 * q^69 + 10 * q^70 - 20 * q^72 + 6 * q^75 - 20 * q^78 + 50 * q^79 - 2 * q^81 - 10 * q^82 + 10 * q^85 + 50 * q^88 + 40 * q^90 - 10 * q^91 + 10 * q^93 - 30 * q^94 + 10 * q^96 + 6 * q^97 + 16 * 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.f.a	$33$	$2$	33.f	33.f	$10$	$8$	$2$	$0.264$	\(\Q(\zeta_{20})\)	None		✓	✓	✓	33.2.f.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots\)