Space of modular forms of level 33 and weight 8

• Label: 33.8
• Level: 33
• Weight: 8
• Dimension: 198
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 640
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(640\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(33))\).

	Total	New	Old
Modular forms	300	218	82
Cusp forms	260	198	62
Eisenstein series	40	20	20

Trace form

198 * q - 12 * q^2 + 49 * q^3 + 174 * q^4 - 780 * q^5 - 1401 * q^6 + 2088 * q^7 + 11600 * q^8 - 4333 * q^9 - 24680 * q^10 - 5642 * q^11 + 11662 * q^12 + 34116 * q^13 + 90318 * q^14 - 40885 * q^15 - 127042 * q^16 - 17262 * q^17 + 102717 * q^18 + 27700 * q^19 - 213190 * q^20 - 188676 * q^21 - 465502 * q^22 + 5636 * q^23 + 508265 * q^24 + 510880 * q^25 + 971126 * q^26 - 274394 * q^27 - 509136 * q^28 - 737440 * q^29 - 476810 * q^30 + 489786 * q^31 + 2408948 * q^32 + 225519 * q^33 - 2797332 * q^34 - 1035320 * q^35 - 324549 * q^36 + 1540818 * q^37 + 3033590 * q^38 + 799988 * q^39 + 1678460 * q^40 - 648144 * q^41 - 397516 * q^42 - 6819564 * q^43 - 10195666 * q^44 - 4685725 * q^45 + 1527496 * q^46 + 3891598 * q^47 + 10568634 * q^48 + 14695114 * q^49 + 10234070 * q^50 + 1344354 * q^51 - 7366832 * q^52 - 7651574 * q^53 - 1338444 * q^54 - 16337890 * q^55 - 15189720 * q^56 - 4146720 * q^57 + 14733540 * q^58 + 1827870 * q^59 - 2017730 * q^60 + 16955836 * q^61 + 10583616 * q^62 + 1989312 * q^63 - 16592266 * q^64 - 7665900 * q^65 + 10284204 * q^66 - 9398882 * q^67 + 8723824 * q^68 + 6664093 * q^69 + 47502620 * q^70 + 14498316 * q^71 - 28296830 * q^72 - 43505804 * q^73 - 44074602 * q^74 - 32730330 * q^75 - 48493200 * q^76 + 2351058 * q^77 + 43122988 * q^78 + 62981600 * q^79 + 55355310 * q^80 + 348683 * q^81 + 55345226 * q^82 + 24739186 * q^83 + 57102612 * q^84 - 32239040 * q^85 - 25505344 * q^86 - 37538640 * q^87 - 144529290 * q^88 - 25376860 * q^89 - 64502420 * q^90 - 56226644 * q^91 - 50393302 * q^92 - 34022697 * q^93 + 18723488 * q^94 + 99060750 * q^95 + 93808684 * q^96 + 131543758 * q^97 + 148165624 * q^98 + 89574197 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(33))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
33.8.a	\(\chi_{33}(1, \cdot)\)	33.8.a.a	1	1
		33.8.a.b	2
		33.8.a.c	2
		33.8.a.d	3
		33.8.a.e	4
33.8.d	\(\chi_{33}(32, \cdot)\)	33.8.d.a	2	1
		33.8.d.b	24
33.8.e	\(\chi_{33}(4, \cdot)\)	33.8.e.a	28	4
		33.8.e.b	28
33.8.f	\(\chi_{33}(2, \cdot)\)	33.8.f.a	104	4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)