Space of modular forms of level 33 and weight 4

• Label: 33.4
• Level: 33
• Weight: 4
• Dimension: 80
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 320
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(320\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(33))\).

	Total	New	Old
Modular forms	140	100	40
Cusp forms	100	80	20
Eisenstein series	40	20	20

Trace form

80 * q - 5 * q^3 - 10 * q^4 + 45 * q^6 + 10 * q^7 - 80 * q^8 - 85 * q^9 - 200 * q^10 - 100 * q^11 - 170 * q^12 - 50 * q^13 + 390 * q^14 + 305 * q^15 + 750 * q^16 + 300 * q^17 + 135 * q^18 - 460 * q^19 - 950 * q^20 - 420 * q^21 - 1270 * q^22 - 380 * q^23 - 1015 * q^24 - 370 * q^25 - 50 * q^26 + 25 * q^27 + 1040 * q^28 + 700 * q^29 + 1930 * q^30 + 1370 * q^31 + 1780 * q^32 + 1800 * q^33 + 1860 * q^34 + 1160 * q^35 + 1215 * q^36 - 50 * q^37 - 650 * q^38 - 1075 * q^39 - 1540 * q^40 - 2220 * q^41 - 2440 * q^42 - 160 * q^43 - 770 * q^44 - 2680 * q^45 - 1800 * q^46 - 1180 * q^47 - 2070 * q^48 - 1990 * q^49 - 1430 * q^50 - 1050 * q^51 - 2400 * q^52 + 320 * q^53 - 540 * q^54 + 1390 * q^55 + 360 * q^56 + 840 * q^57 - 1700 * q^58 - 1020 * q^59 + 3190 * q^60 + 1150 * q^61 + 2760 * q^62 + 4125 * q^63 + 5990 * q^64 + 3360 * q^65 + 7140 * q^66 + 3320 * q^67 + 4880 * q^68 + 3310 * q^69 + 5100 * q^70 + 1860 * q^71 - 110 * q^72 + 5450 * q^73 + 1950 * q^74 - 1080 * q^75 - 4000 * q^76 - 900 * q^77 - 7340 * q^78 - 3610 * q^79 - 9810 * q^80 - 7825 * q^81 - 12770 * q^82 - 7720 * q^83 - 11580 * q^84 - 12410 * q^85 - 5960 * q^86 - 5220 * q^87 - 11290 * q^88 - 3500 * q^89 + 7600 * q^90 + 2190 * q^91 + 11050 * q^92 + 6105 * q^93 + 13040 * q^94 + 3600 * q^95 + 14140 * q^96 + 5960 * q^97 + 5060 * q^98 + 4865 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)

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
33.4.a	\(\chi_{33}(1, \cdot)\)	33.4.a.a	1	1
		33.4.a.b	1
		33.4.a.c	2
		33.4.a.d	2
33.4.d	\(\chi_{33}(32, \cdot)\)	33.4.d.a	2	1
		33.4.d.b	8
33.4.e	\(\chi_{33}(4, \cdot)\)	33.4.e.a	4	4
		33.4.e.b	8
		33.4.e.c	12
33.4.f	\(\chi_{33}(2, \cdot)\)	33.4.f.a	40	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces

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