Space of modular forms of level 33 and weight 6

• Label: 33.6
• Level: 33
• Weight: 6
• Dimension: 138
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(33))\).

	Total	New	Old
Modular forms	220	158	62
Cusp forms	180	138	42
Eisenstein series	40	20	20

Trace form

138 * q + 12 * q^2 - 23 * q^3 - 18 * q^4 - 12 * q^5 + 123 * q^6 - 520 * q^7 - 656 * q^8 + 383 * q^9 + 2072 * q^10 + 1454 * q^11 + 238 * q^12 - 2296 * q^13 + 510 * q^14 - 3853 * q^15 - 14018 * q^16 - 5274 * q^17 + 4977 * q^18 + 5572 * q^19 + 17002 * q^20 + 9540 * q^21 + 21746 * q^22 + 7060 * q^23 - 3559 * q^24 - 6592 * q^25 - 24794 * q^26 + 8602 * q^27 - 46240 * q^28 - 21896 * q^29 - 11402 * q^30 + 24410 * q^31 + 78100 * q^32 - 1869 * q^33 - 11236 * q^34 - 55480 * q^35 - 58293 * q^36 - 48430 * q^37 - 45722 * q^38 + 11876 * q^39 + 50284 * q^40 + 86040 * q^41 + 145940 * q^42 + 72292 * q^43 + 78046 * q^44 + 35213 * q^45 - 47720 * q^46 - 23266 * q^47 - 84942 * q^48 - 97746 * q^49 - 194258 * q^50 - 168726 * q^51 - 5984 * q^52 - 111610 * q^53 + 37908 * q^54 + 117854 * q^55 + 344040 * q^56 + 312018 * q^57 + 270916 * q^58 + 26598 * q^59 + 9958 * q^60 - 61616 * q^61 + 10320 * q^62 - 161640 * q^63 - 576714 * q^64 - 291396 * q^65 - 586956 * q^66 - 86074 * q^67 - 144976 * q^68 - 38285 * q^69 + 416860 * q^70 + 343116 * q^71 + 388834 * q^72 + 234640 * q^73 - 18810 * q^74 + 270702 * q^75 + 8368 * q^76 - 281850 * q^77 + 141964 * q^78 - 401280 * q^79 - 30258 * q^80 - 365017 * q^81 - 274510 * q^82 + 63866 * q^83 + 74340 * q^84 + 680436 * q^85 + 182608 * q^86 + 370656 * q^87 + 1238902 * q^88 + 427492 * q^89 + 414292 * q^90 + 1133540 * q^91 + 926650 * q^92 + 113295 * q^93 - 638944 * q^94 - 477378 * q^95 - 1649900 * q^96 - 1950194 * q^97 - 2674864 * q^98 - 1074091 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.6.a	\(\chi_{33}(1, \cdot)\)	33.6.a.a	1	1
		33.6.a.b	1
		33.6.a.c	2
		33.6.a.d	2
		33.6.a.e	2
33.6.d	\(\chi_{33}(32, \cdot)\)	33.6.d.a	2	1
		33.6.d.b	16
33.6.e	\(\chi_{33}(4, \cdot)\)	33.6.e.a	20	4
		33.6.e.b	20
33.6.f	\(\chi_{33}(2, \cdot)\)	33.6.f.a	72	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 1}\)