Space of modular forms of level 189 and weight 6

• Label: 189.6
• Level: 189
• Weight: 6
• Dimension: 4826
• Nonzero newspaces: 16
• Sturm bound: 15552
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(15552\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(189))\).

	Total	New	Old
Modular forms	6660	4986	1674
Cusp forms	6300	4826	1474
Eisenstein series	360	160	200

Trace form

4826 * q - 6 * q^2 - 24 * q^3 - 168 * q^4 + 318 * q^5 + 216 * q^6 - 171 * q^7 - 2694 * q^8 - 684 * q^9 - 120 * q^10 + 642 * q^11 + 5502 * q^12 + 4322 * q^13 + 3249 * q^14 - 4050 * q^15 - 7024 * q^16 - 14064 * q^17 + 162 * q^18 - 6580 * q^19 - 21036 * q^20 - 5460 * q^21 + 20790 * q^22 + 33294 * q^23 + 36936 * q^24 - 8932 * q^25 - 14316 * q^26 + 16182 * q^27 + 22550 * q^28 + 60564 * q^29 + 12870 * q^30 - 6718 * q^31 - 85416 * q^32 - 101304 * q^33 - 6108 * q^34 - 6792 * q^35 + 7128 * q^36 - 34758 * q^37 + 35898 * q^38 + 27906 * q^39 - 63564 * q^40 + 79932 * q^41 + 64386 * q^42 + 1806 * q^43 - 177384 * q^44 - 185022 * q^45 + 34320 * q^46 - 150702 * q^47 - 128166 * q^48 + 208001 * q^49 + 478524 * q^50 + 181062 * q^51 - 28012 * q^52 - 87234 * q^53 + 339408 * q^54 - 285684 * q^55 - 499599 * q^56 - 164478 * q^57 - 173616 * q^58 + 66510 * q^59 + 142920 * q^60 + 514958 * q^61 + 913962 * q^62 + 340389 * q^63 + 743178 * q^64 + 530274 * q^65 + 273762 * q^66 - 359060 * q^67 - 943374 * q^68 - 318852 * q^69 - 931317 * q^70 - 1145982 * q^71 - 2038284 * q^72 - 583060 * q^73 - 1324746 * q^74 - 382344 * q^75 + 607424 * q^76 + 875307 * q^77 + 1885428 * q^78 + 1378462 * q^79 + 2581530 * q^80 + 857196 * q^81 + 254964 * q^82 + 480156 * q^83 + 522354 * q^84 + 23298 * q^85 - 1167510 * q^86 - 608382 * q^87 - 1821096 * q^88 - 1134084 * q^89 - 654768 * q^90 + 199013 * q^91 - 915126 * q^92 - 1780194 * q^93 + 462288 * q^94 - 413550 * q^95 - 2331432 * q^96 + 871922 * q^97 + 264780 * q^98 + 56574 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(189))\)

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
189.6.a	\(\chi_{189}(1, \cdot)\)	189.6.a.a	1	1
		189.6.a.b	1
		189.6.a.c	1
		189.6.a.d	1
		189.6.a.e	2
		189.6.a.f	2
		189.6.a.g	2
		189.6.a.h	4
		189.6.a.i	4
		189.6.a.j	4
		189.6.a.k	4
		189.6.a.l	4
		189.6.a.m	5
		189.6.a.n	5
189.6.c	\(\chi_{189}(188, \cdot)\)	189.6.c.a	2	1
		189.6.c.b	24
		189.6.c.c	28
189.6.e	\(\chi_{189}(109, \cdot)\)	n/a	106	2
189.6.f	\(\chi_{189}(64, \cdot)\)	189.6.f.a	30	2
		189.6.f.b	30
189.6.g	\(\chi_{189}(100, \cdot)\)	189.6.g.a	76	2
189.6.h	\(\chi_{189}(37, \cdot)\)	189.6.h.a	76	2
189.6.i	\(\chi_{189}(143, \cdot)\)	189.6.i.a	76	2
189.6.o	\(\chi_{189}(62, \cdot)\)	189.6.o.a	76	2
189.6.p	\(\chi_{189}(26, \cdot)\)	n/a	106	2
189.6.s	\(\chi_{189}(17, \cdot)\)	189.6.s.a	76	2
189.6.u	\(\chi_{189}(4, \cdot)\)	n/a	708	6
189.6.v	\(\chi_{189}(22, \cdot)\)	n/a	540	6
189.6.w	\(\chi_{189}(25, \cdot)\)	n/a	708	6
189.6.ba	\(\chi_{189}(5, \cdot)\)	n/a	708	6
189.6.bd	\(\chi_{189}(47, \cdot)\)	n/a	708	6
189.6.be	\(\chi_{189}(20, \cdot)\)	n/a	708	6

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(189))\) into lower level spaces

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