Space of modular forms of level 33, weight 3, and Character 33.g

• Label: 33.3.g
• Level: $33$
• Weight: $3$
• Character orbit: 33.g
• Rep. character: $\chi_{33}(7,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	33.g (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(33, [\chi])\).

	Total	New	Old
Modular forms	40	16	24
Cusp forms	24	16	8
Eisenstein series	16	0	16

Trace form

16 * q + 20 * q^4 - 4 * q^5 - 30 * q^7 - 40 * q^8 - 12 * q^9 - 10 * q^11 - 24 * q^12 + 30 * q^13 - 2 * q^14 - 24 * q^15 + 16 * q^16 - 10 * q^17 - 30 * q^18 + 42 * q^20 + 42 * q^22 + 132 * q^23 + 90 * q^24 - 2 * q^25 + 46 * q^26 - 50 * q^28 + 160 * q^29 + 180 * q^30 + 10 * q^31 + 12 * q^33 - 368 * q^34 - 320 * q^35 + 60 * q^36 - 126 * q^37 - 130 * q^38 + 30 * q^40 - 120 * q^41 - 204 * q^42 - 206 * q^44 - 12 * q^45 + 50 * q^46 - 150 * q^47 - 96 * q^48 + 210 * q^49 + 330 * q^50 - 60 * q^51 + 110 * q^52 + 342 * q^53 + 244 * q^55 + 524 * q^56 + 60 * q^57 + 150 * q^58 + 110 * q^59 + 36 * q^60 - 90 * q^61 + 40 * q^62 + 90 * q^63 - 168 * q^64 + 48 * q^66 + 36 * q^67 + 80 * q^68 + 210 * q^69 + 340 * q^70 - 236 * q^71 - 150 * q^72 - 350 * q^73 - 730 * q^74 - 408 * q^75 - 390 * q^77 - 312 * q^78 + 210 * q^79 - 806 * q^80 - 36 * q^81 + 114 * q^82 - 190 * q^83 - 180 * q^84 + 110 * q^85 + 736 * q^86 + 144 * q^88 + 76 * q^89 + 60 * q^90 + 306 * q^91 - 150 * q^92 + 144 * q^93 - 350 * q^94 + 430 * q^95 + 450 * q^96 - 354 * q^97 + 180 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(33, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.3.g.a	$33$	$3$	33.g	11.d	$10$	$16$	$4$	$0.899$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	33.3.g.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-30\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(1+\beta _{2}-\beta _{5}+\beta _{7}+\beta _{8})q^{2}-\beta _{14}q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(33, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)