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

• Label: 33.3.h
• Level: $33$
• Weight: $3$
• Character orbit: 33.h
• Rep. character: $\chi_{33}(5,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	33.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
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	40	40	0
Cusp forms	24	24	0
Eisenstein series	16	16	0

Trace form

24 * q - 6 * q^3 + 2 * q^4 - 23 * q^6 + 2 * q^7 - 26 * q^9 - 56 * q^10 + 58 * q^12 - 10 * q^13 + 32 * q^15 - 98 * q^16 - 3 * q^18 - 22 * q^19 + 76 * q^21 + 20 * q^22 + 111 * q^24 + 92 * q^25 + 36 * q^27 + 342 * q^28 - 132 * q^30 + 106 * q^31 - 169 * q^33 - 84 * q^34 - 213 * q^36 - 30 * q^37 - 238 * q^39 - 242 * q^40 - 172 * q^42 - 420 * q^43 + 8 * q^45 + 2 * q^46 + 50 * q^48 - 180 * q^49 + 171 * q^51 + 362 * q^52 + 1046 * q^54 + 144 * q^55 + 417 * q^57 + 70 * q^58 + 234 * q^60 + 210 * q^61 - 134 * q^63 + 262 * q^64 - 360 * q^66 + 344 * q^67 - 42 * q^69 - 280 * q^70 - 842 * q^72 - 158 * q^73 - 157 * q^75 - 1164 * q^76 - 452 * q^78 - 774 * q^79 - 230 * q^81 - 72 * q^82 + 294 * q^84 + 282 * q^85 + 792 * q^87 + 798 * q^88 + 160 * q^90 + 458 * q^91 + 26 * q^93 + 1042 * q^94 - 662 * q^96 + 588 * q^97 - 490 * 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.h.a	$33$	$3$	33.h	33.h	$10$	$8$	$2$	$0.899$	\(\Q(\zeta_{20})\)	None		✓			33.3.h.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\zeta_{20}q^{2}+(2+2\zeta_{20}-2\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
33.3.h.b	$33$	$3$	33.h	33.h	$10$	$16$	$4$	$0.899$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		33.3.h.b	$4$	$0$	\(0\)	\(-10\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)