Space of modular forms of level 33, weight 8, and Character 33.e

• Label: 33.8.e
• Level: $33$
• Weight: $8$
• Character orbit: 33.e
• Rep. character: $\chi_{33}(4,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(33, [\chi])\).

	Total	New	Old
Modular forms	120	56	64
Cusp forms	104	56	48
Eisenstein series	16	0	16

Trace form

56 * q - 28 * q^2 - 532 * q^4 - 4 * q^5 + 432 * q^6 + 1206 * q^7 + 6524 * q^8 - 10206 * q^9 - 11992 * q^10 - 5642 * q^11 - 15336 * q^12 + 28134 * q^13 + 59594 * q^14 - 45630 * q^15 - 149344 * q^16 + 19958 * q^17 + 30618 * q^18 + 83484 * q^19 - 212994 * q^20 - 148176 * q^21 - 251198 * q^22 - 28476 * q^23 + 232146 * q^24 - 74236 * q^25 + 806554 * q^26 + 17154 * q^28 - 295276 * q^29 - 556956 * q^30 + 7716 * q^31 + 2422824 * q^32 - 97470 * q^33 - 2772832 * q^34 + 16800 * q^35 - 387828 * q^36 + 1481262 * q^37 + 3830870 * q^38 - 30672 * q^39 + 3214478 * q^40 - 1679860 * q^41 + 920700 * q^42 - 5465072 * q^43 - 11228522 * q^44 - 2916 * q^45 + 4588098 * q^46 + 3779558 * q^47 + 3022704 * q^48 + 6895888 * q^49 + 7584342 * q^50 + 956448 * q^51 - 2017290 * q^52 - 3369590 * q^53 - 1259712 * q^54 - 16726400 * q^55 - 24509724 * q^56 + 2770200 * q^57 + 15512158 * q^58 - 2806274 * q^59 + 9893988 * q^60 + 5058462 * q^61 + 19627304 * q^62 + 879174 * q^63 - 25458512 * q^64 - 10472380 * q^65 - 8919720 * q^66 - 10376948 * q^67 + 18356216 * q^68 - 351054 * q^69 + 26826716 * q^70 + 13417956 * q^71 - 3868074 * q^72 - 6542760 * q^73 - 44806722 * q^74 - 14339160 * q^75 - 26226176 * q^76 + 2281846 * q^77 + 32745168 * q^78 + 6953634 * q^79 + 71198962 * q^80 - 7440174 * q^81 + 44813122 * q^82 + 8643322 * q^83 - 16402500 * q^84 - 16047290 * q^85 + 8641064 * q^86 - 34485912 * q^87 - 11218976 * q^88 - 30639796 * q^89 - 708588 * q^90 - 5396434 * q^91 - 79168370 * q^92 + 21179340 * q^93 - 6829706 * q^94 + 73306758 * q^95 + 28946430 * q^96 + 8347890 * q^97 + 123577960 * q^98 + 5079672 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(33, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.8.e.a	$33$	$8$	33.e	11.c	$5$	$28$	$7$	$10.309$		None		✓			33.8.e.a	$2$	$0$	\(-22\)	\(189\)	\(-777\)	\(-83\)		$\mathrm{SU}(2)[C_{5}]$
33.8.e.b	$33$	$8$	33.e	11.c	$5$	$28$	$7$	$10.309$		None		✓			33.8.e.b	$2$	$0$	\(-6\)	\(-189\)	\(773\)	\(1289\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{8}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(33, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)