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

• Label: 33.3.b
• Level: $33$
• Weight: $3$
• Character orbit: 33.b
• Rep. character: $\chi_{33}(23,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	10	6	4
Cusp forms	6	6	0
Eisenstein series	4	0	4

Trace form

6 * q + q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 11 * q^9 + 36 * q^10 - 28 * q^12 + 13 * q^15 - 12 * q^16 + 38 * q^18 - 48 * q^19 - 86 * q^21 + 24 * q^24 + 48 * q^25 + 34 * q^27 + 48 * q^28 + 142 * q^30 - 6 * q^31 - 11 * q^33 + 24 * q^34 - 212 * q^36 - 30 * q^37 - 32 * q^39 - 168 * q^40 - 68 * q^42 + 180 * q^43 + 17 * q^45 - 132 * q^46 + 140 * q^48 - 30 * q^49 + 214 * q^51 - 192 * q^52 - 176 * q^54 + 66 * q^55 + 108 * q^57 + 480 * q^58 + 56 * q^60 + 14 * q^63 + 228 * q^64 - 110 * q^66 - 54 * q^67 - 253 * q^69 - 360 * q^70 + 72 * q^72 - 432 * q^73 - 238 * q^75 + 264 * q^76 - 128 * q^78 - 156 * q^79 + 275 * q^81 - 48 * q^82 + 416 * q^84 + 108 * q^85 - 252 * q^87 + 132 * q^88 + 410 * q^90 + 192 * q^91 - 131 * q^93 - 312 * q^94 + 272 * q^96 + 342 * q^97 - 55 * 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.b.a	$33$	$3$	33.b	3.b	$2$	$2$	$2$	$0.899$	\(\Q(\sqrt{-11}) \)	None		✓			33.3.b.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(-16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+3q^{3}-7q^{4}+2\beta q^{5}-3\beta q^{6}+\cdots\)
33.3.b.b	$33$	$3$	33.b	3.b	$2$	$4$	$4$	$0.899$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓	✓		33.3.b.b	$2$	$0$	\(0\)	\(-5\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{3}+\cdots\)