Space of modular forms of level 189 and weight 3

• Label: 189.3
• Level: 189
• Weight: 3
• Dimension: 1882
• Nonzero newspaces: 16
• Newform subspaces: 38
• Sturm bound: 7776
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 38 \)
Sturm bound:			\(7776\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(189))\).

	Total	New	Old
Modular forms	2772	2042	730
Cusp forms	2412	1882	530
Eisenstein series	360	160	200

Trace form

1882 * q - 18 * q^2 - 24 * q^3 - 16 * q^4 + 18 * q^5 - 31 * q^7 - 30 * q^8 - 36 * q^9 - 48 * q^10 - 18 * q^11 - 6 * q^12 + 18 * q^13 + 69 * q^14 - 54 * q^15 + 64 * q^16 + 48 * q^17 - 162 * q^18 - 24 * q^19 - 456 * q^20 - 168 * q^21 - 234 * q^22 - 414 * q^23 - 324 * q^24 - 170 * q^25 - 144 * q^26 + 144 * q^27 - 146 * q^28 + 336 * q^29 + 450 * q^30 + 138 * q^31 + 924 * q^32 + 378 * q^33 + 372 * q^34 + 444 * q^35 + 648 * q^36 + 22 * q^37 + 258 * q^38 - 66 * q^39 + 12 * q^40 - 516 * q^41 - 522 * q^42 - 218 * q^43 - 1524 * q^44 - 990 * q^45 - 672 * q^46 - 1206 * q^47 - 1590 * q^48 - 461 * q^49 - 2556 * q^50 - 702 * q^51 - 1500 * q^52 - 1662 * q^53 - 792 * q^54 - 708 * q^55 - 1755 * q^56 - 48 * q^57 - 312 * q^58 + 648 * q^59 + 1224 * q^60 + 282 * q^61 + 1746 * q^62 + 675 * q^63 + 194 * q^64 + 1626 * q^65 + 1386 * q^66 - 136 * q^67 + 2358 * q^68 + 396 * q^69 + 1047 * q^70 + 978 * q^71 + 324 * q^72 + 1260 * q^73 + 2454 * q^74 + 624 * q^75 + 792 * q^76 + 1563 * q^77 + 720 * q^78 + 254 * q^79 + 2334 * q^80 - 108 * q^81 + 588 * q^82 - 120 * q^83 + 552 * q^84 + 186 * q^85 - 6 * q^86 + 522 * q^87 + 1800 * q^88 - 222 * q^89 - 612 * q^90 - 171 * q^91 + 162 * q^92 - 1218 * q^93 + 1128 * q^94 - 1686 * q^95 - 576 * q^96 + 534 * q^97 - 1464 * q^98 - 1098 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(189))\)

We only show spaces with odd 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
189.3.b	\(\chi_{189}(134, \cdot)\)	189.3.b.a	4	1
		189.3.b.b	4
		189.3.b.c	8
189.3.d	\(\chi_{189}(55, \cdot)\)	189.3.d.a	2	1
		189.3.d.b	2
		189.3.d.c	2
		189.3.d.d	8
		189.3.d.e	8
189.3.j	\(\chi_{189}(44, \cdot)\)	189.3.j.a	6	2
		189.3.j.b	22
189.3.k	\(\chi_{189}(10, \cdot)\)	189.3.k.a	28	2
189.3.l	\(\chi_{189}(118, \cdot)\)	189.3.l.a	28	2
189.3.m	\(\chi_{189}(82, \cdot)\)	189.3.m.a	2	2
		189.3.m.b	4
		189.3.m.c	4
		189.3.m.d	6
		189.3.m.e	6
		189.3.m.f	8
		189.3.m.g	12
189.3.n	\(\chi_{189}(170, \cdot)\)	189.3.n.a	6	2
		189.3.n.b	22
189.3.q	\(\chi_{189}(53, \cdot)\)	189.3.q.a	2	2
		189.3.q.b	2
		189.3.q.c	2
		189.3.q.d	4
		189.3.q.e	4
		189.3.q.f	4
		189.3.q.g	4
		189.3.q.h	4
		189.3.q.i	16
189.3.r	\(\chi_{189}(8, \cdot)\)	189.3.r.a	24	2
189.3.t	\(\chi_{189}(73, \cdot)\)	189.3.t.a	28	2
189.3.x	\(\chi_{189}(40, \cdot)\)	189.3.x.a	276	6
189.3.y	\(\chi_{189}(13, \cdot)\)	189.3.y.a	276	6
189.3.z	\(\chi_{189}(31, \cdot)\)	189.3.z.a	276	6
189.3.bb	\(\chi_{189}(29, \cdot)\)	189.3.bb.a	216	6
189.3.bc	\(\chi_{189}(2, \cdot)\)	189.3.bc.a	276	6
189.3.bf	\(\chi_{189}(11, \cdot)\)	189.3.bf.a	276	6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(189))\) into lower level spaces

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