Space of modular forms of level 133 and weight 2

• Label: 133.2
• Level: 133
• Weight: 2
• Dimension: 599
• Nonzero newspaces: 16
• Newform subspaces: 39
• Sturm bound: 2880
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 39 \)
Sturm bound:			\(2880\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(133))\).

	Total	New	Old
Modular forms	828	771	57
Cusp forms	613	599	14
Eisenstein series	215	172	43

Trace form

599 * q - 39 * q^2 - 40 * q^3 - 43 * q^4 - 42 * q^5 - 48 * q^6 - 46 * q^7 - 105 * q^8 - 49 * q^9 - 54 * q^10 - 48 * q^11 - 40 * q^12 - 26 * q^13 - 30 * q^14 - 78 * q^15 + 5 * q^16 - 36 * q^17 - 3 * q^18 - 13 * q^19 - 42 * q^20 - 28 * q^21 - 72 * q^22 - 42 * q^23 - 24 * q^24 - 31 * q^25 - 42 * q^26 - 34 * q^27 - 13 * q^28 - 84 * q^29 + 18 * q^30 - 32 * q^31 - 9 * q^32 + 24 * q^33 - 15 * q^35 + 35 * q^36 - 20 * q^37 + 33 * q^38 - 20 * q^39 + 36 * q^40 - 42 * q^41 + 33 * q^42 - 56 * q^43 + 24 * q^44 + 48 * q^45 + 54 * q^46 + 6 * q^47 + 92 * q^48 - 28 * q^49 + 15 * q^50 - 2 * q^52 - 18 * q^53 + 6 * q^54 - 36 * q^55 + 57 * q^56 - 76 * q^57 - 90 * q^58 - 6 * q^59 + 102 * q^60 + 34 * q^61 + 66 * q^62 + 26 * q^63 + 59 * q^64 + 78 * q^65 + 108 * q^66 + 82 * q^67 + 90 * q^68 + 66 * q^69 + 81 * q^70 - 36 * q^71 + 165 * q^72 + 58 * q^73 + 30 * q^74 + 26 * q^75 + 11 * q^76 - 3 * q^77 + 30 * q^78 + 88 * q^79 + 102 * q^80 + 77 * q^81 + 180 * q^82 + 6 * q^83 + 143 * q^84 + 18 * q^85 + 30 * q^86 + 132 * q^87 + 108 * q^88 + 36 * q^89 + 144 * q^90 + 25 * q^91 - 24 * q^92 + 40 * q^93 + 54 * q^94 - 24 * q^95 + 108 * q^96 - 8 * q^97 + 123 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)

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
133.2.a	\(\chi_{133}(1, \cdot)\)	133.2.a.a	2	1
		133.2.a.b	2
		133.2.a.c	2
		133.2.a.d	3
133.2.c	\(\chi_{133}(132, \cdot)\)	133.2.c.a	2	1
		133.2.c.b	4
		133.2.c.c	4
133.2.e	\(\chi_{133}(64, \cdot)\)	133.2.e.a	4	2
		133.2.e.b	6
		133.2.e.c	10
133.2.f	\(\chi_{133}(39, \cdot)\)	133.2.f.a	2	2
		133.2.f.b	4
		133.2.f.c	4
		133.2.f.d	14
133.2.g	\(\chi_{133}(30, \cdot)\)	133.2.g.a	24	2
133.2.h	\(\chi_{133}(11, \cdot)\)	133.2.h.a	24	2
133.2.i	\(\chi_{133}(12, \cdot)\)	133.2.i.a	2	2
		133.2.i.b	2
		133.2.i.c	4
		133.2.i.d	16
133.2.o	\(\chi_{133}(75, \cdot)\)	133.2.o.a	4	2
		133.2.o.b	4
		133.2.o.c	4
		133.2.o.d	6
		133.2.o.e	6
133.2.p	\(\chi_{133}(27, \cdot)\)	133.2.p.a	4	2
		133.2.p.b	4
		133.2.p.c	12
133.2.s	\(\chi_{133}(31, \cdot)\)	133.2.s.a	2	2
		133.2.s.b	2
		133.2.s.c	4
		133.2.s.d	16
133.2.u	\(\chi_{133}(9, \cdot)\)	133.2.u.a	66	6
133.2.v	\(\chi_{133}(36, \cdot)\)	133.2.v.a	30	6
		133.2.v.b	30
133.2.w	\(\chi_{133}(4, \cdot)\)	133.2.w.a	66	6
133.2.ba	\(\chi_{133}(13, \cdot)\)	133.2.ba.a	72	6
133.2.bb	\(\chi_{133}(3, \cdot)\)	133.2.bb.a	66	6
133.2.bf	\(\chi_{133}(10, \cdot)\)	133.2.bf.a	66	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(133))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(133)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)