Space of modular forms of level 189 and weight 2

• Label: 189.2
• Level: 189
• Weight: 2
• Dimension: 902
• Nonzero newspaces: 16
• Newform subspaces: 37
• Sturm bound: 5184
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 37 \)
Sturm bound:			\(5184\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(189))\).

	Total	New	Old
Modular forms	1476	1062	414
Cusp forms	1117	902	215
Eisenstein series	359	160	199

Trace form

902 * q - 12 * q^2 - 24 * q^3 - 26 * q^4 - 18 * q^5 - 36 * q^6 - 35 * q^7 - 60 * q^8 - 36 * q^9 - 36 * q^10 - 30 * q^11 - 60 * q^12 - 42 * q^13 - 51 * q^14 - 90 * q^15 - 70 * q^16 - 60 * q^17 - 54 * q^18 - 36 * q^19 - 60 * q^20 - 24 * q^21 - 114 * q^22 - 18 * q^23 - 52 * q^25 - 18 * q^27 - 106 * q^28 - 48 * q^29 - 18 * q^30 - 54 * q^31 - 78 * q^32 - 36 * q^33 - 96 * q^34 - 72 * q^35 - 108 * q^36 - 82 * q^37 - 168 * q^38 - 102 * q^39 - 120 * q^40 - 108 * q^41 - 54 * q^42 - 130 * q^43 - 108 * q^44 - 18 * q^45 - 96 * q^46 - 30 * q^47 + 102 * q^48 - 43 * q^49 + 78 * q^50 + 54 * q^51 + 12 * q^52 + 138 * q^53 + 180 * q^54 + 12 * q^55 + 267 * q^56 + 6 * q^57 + 48 * q^58 + 150 * q^59 + 180 * q^60 - 6 * q^61 + 270 * q^62 + 81 * q^63 + 100 * q^64 + 150 * q^65 + 126 * q^66 + 28 * q^67 + 276 * q^68 + 36 * q^69 + 57 * q^70 - 30 * q^71 + 108 * q^72 + 12 * q^73 + 6 * q^74 - 24 * q^75 + 42 * q^76 - 21 * q^77 - 36 * q^78 - 26 * q^79 - 6 * q^80 - 108 * q^81 - 120 * q^82 - 180 * q^83 - 42 * q^84 - 102 * q^85 - 258 * q^86 - 54 * q^87 - 42 * q^88 - 156 * q^89 - 72 * q^90 - 123 * q^91 - 126 * q^92 + 42 * q^93 - 132 * q^94 - 78 * q^95 - 36 * q^96 - 90 * q^97 - 96 * q^98 - 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)

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
189.2.a	\(\chi_{189}(1, \cdot)\)	189.2.a.a	1	1
		189.2.a.b	1
		189.2.a.c	1
		189.2.a.d	1
		189.2.a.e	2
		189.2.a.f	2
189.2.c	\(\chi_{189}(188, \cdot)\)	189.2.c.a	2	1
		189.2.c.b	4
		189.2.c.c	4
189.2.e	\(\chi_{189}(109, \cdot)\)	189.2.e.a	2	2
		189.2.e.b	2
		189.2.e.c	2
		189.2.e.d	4
		189.2.e.e	6
		189.2.e.f	6
189.2.f	\(\chi_{189}(64, \cdot)\)	189.2.f.a	6	2
		189.2.f.b	6
189.2.g	\(\chi_{189}(100, \cdot)\)	189.2.g.a	2	2
		189.2.g.b	10
189.2.h	\(\chi_{189}(37, \cdot)\)	189.2.h.a	2	2
		189.2.h.b	10
189.2.i	\(\chi_{189}(143, \cdot)\)	189.2.i.a	2	2
		189.2.i.b	10
189.2.o	\(\chi_{189}(62, \cdot)\)	189.2.o.a	12	2
189.2.p	\(\chi_{189}(26, \cdot)\)	189.2.p.a	2	2
		189.2.p.b	4
		189.2.p.c	4
		189.2.p.d	12
189.2.s	\(\chi_{189}(17, \cdot)\)	189.2.s.a	2	2
		189.2.s.b	10
189.2.u	\(\chi_{189}(4, \cdot)\)	189.2.u.a	132	6
189.2.v	\(\chi_{189}(22, \cdot)\)	189.2.v.a	54	6
		189.2.v.b	54
189.2.w	\(\chi_{189}(25, \cdot)\)	189.2.w.a	132	6
189.2.ba	\(\chi_{189}(5, \cdot)\)	189.2.ba.a	132	6
189.2.bd	\(\chi_{189}(47, \cdot)\)	189.2.bd.a	132	6
189.2.be	\(\chi_{189}(20, \cdot)\)	189.2.be.a	132	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(189))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(189)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)