Space of modular forms of level 143 and weight 2

• Label: 143.2
• Level: 143
• Weight: 2
• Dimension: 715
• Nonzero newspaces: 12
• Newform subspaces: 19
• Sturm bound: 3360
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(3360\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(143))\).

	Total	New	Old
Modular forms	960	915	45
Cusp forms	721	715	6
Eisenstein series	239	200	39

Trace form

715 * q - 47 * q^2 - 50 * q^3 - 59 * q^4 - 56 * q^5 - 64 * q^6 - 48 * q^7 - 45 * q^8 - 41 * q^9 - 32 * q^10 - 51 * q^11 - 80 * q^12 - 41 * q^13 - 104 * q^14 - 46 * q^15 - 31 * q^16 - 44 * q^17 - 29 * q^18 - 28 * q^19 - 28 * q^20 - 32 * q^21 - 23 * q^22 - 106 * q^23 + 12 * q^24 - 29 * q^25 - 19 * q^26 - 74 * q^27 + 4 * q^28 - 24 * q^29 + 20 * q^30 - 42 * q^31 + 5 * q^32 - 14 * q^33 - 74 * q^34 - 8 * q^35 + 37 * q^36 - 58 * q^37 - 24 * q^38 - 32 * q^39 - 42 * q^40 + 16 * q^41 + 44 * q^42 + 12 * q^43 + 13 * q^44 - 32 * q^45 + 44 * q^46 - 28 * q^47 + 36 * q^48 + 17 * q^49 + 29 * q^50 + 32 * q^51 + 19 * q^52 - 42 * q^53 + 56 * q^54 + 4 * q^55 + 20 * q^57 + 12 * q^58 - 34 * q^59 + 112 * q^60 - 20 * q^61 + 52 * q^62 + 36 * q^63 + 87 * q^64 + 32 * q^65 + 8 * q^66 - 50 * q^67 + 80 * q^68 + 10 * q^69 + 76 * q^70 + 6 * q^71 + 129 * q^72 + 6 * q^73 + 96 * q^74 + 64 * q^75 + 92 * q^76 + 32 * q^77 + 76 * q^78 - 36 * q^79 + 164 * q^80 + 37 * q^81 + 16 * q^82 + 36 * q^83 + 156 * q^84 + 34 * q^85 + 48 * q^86 + 72 * q^87 + 105 * q^88 - 36 * q^89 + 154 * q^90 + 52 * q^91 + 28 * q^92 + 106 * q^93 + 128 * q^94 + 48 * q^95 + 208 * q^96 + 28 * q^97 + 57 * q^98 + 87 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)

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
143.2.a	\(\chi_{143}(1, \cdot)\)	143.2.a.a	1	1
		143.2.a.b	4
		143.2.a.c	6
143.2.b	\(\chi_{143}(12, \cdot)\)	143.2.b.a	12	1
143.2.e	\(\chi_{143}(100, \cdot)\)	143.2.e.a	6	2
		143.2.e.b	6
		143.2.e.c	12
143.2.g	\(\chi_{143}(21, \cdot)\)	143.2.g.a	24	2
143.2.h	\(\chi_{143}(14, \cdot)\)	143.2.h.a	4	4
		143.2.h.b	16
		143.2.h.c	28
143.2.j	\(\chi_{143}(23, \cdot)\)	143.2.j.a	4	2
		143.2.j.b	16
143.2.n	\(\chi_{143}(25, \cdot)\)	143.2.n.a	48	4
143.2.o	\(\chi_{143}(32, \cdot)\)	143.2.o.a	48	4
143.2.q	\(\chi_{143}(3, \cdot)\)	143.2.q.a	96	8
143.2.s	\(\chi_{143}(8, \cdot)\)	143.2.s.a	96	8
143.2.u	\(\chi_{143}(4, \cdot)\)	143.2.u.a	96	8
143.2.w	\(\chi_{143}(2, \cdot)\)	143.2.w.a	192	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(143))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(143)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)