Space of modular forms of level 147 and weight 8

• Label: 147.8
• Level: 147
• Weight: 8
• Dimension: 3901
• Nonzero newspaces: 8
• Sturm bound: 12544
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(12544\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(147))\).

	Total	New	Old
Modular forms	5608	3997	1611
Cusp forms	5368	3901	1467
Eisenstein series	240	96	144

Trace form

3901 * q + 6 * q^2 + 12 * q^3 - 1146 * q^4 + 378 * q^5 + 2409 * q^6 + 628 * q^7 - 8628 * q^8 + 3780 * q^9 - 34038 * q^10 + 4056 * q^11 + 44751 * q^12 + 11296 * q^13 + 39288 * q^14 - 42393 * q^15 - 188606 * q^16 - 95622 * q^17 - 46299 * q^18 + 43054 * q^19 + 889392 * q^20 + 20919 * q^21 - 947046 * q^22 - 652392 * q^23 + 160323 * q^24 + 265045 * q^25 + 1468224 * q^26 + 137760 * q^27 + 531948 * q^28 - 295626 * q^29 - 831261 * q^30 - 2243870 * q^31 - 1225788 * q^32 - 998085 * q^33 + 1334058 * q^34 + 1293726 * q^35 + 2050041 * q^36 + 3362684 * q^37 - 6638772 * q^38 - 6644934 * q^39 - 7620906 * q^40 + 1196814 * q^41 + 2825853 * q^42 + 3243378 * q^43 + 20937024 * q^44 + 9821175 * q^45 - 5071266 * q^46 - 11047032 * q^47 - 12269232 * q^48 - 18707898 * q^49 - 13707042 * q^50 - 12951255 * q^51 + 8642718 * q^52 + 13086186 * q^53 + 13369677 * q^54 + 40599288 * q^55 + 41657262 * q^56 + 19647087 * q^57 + 20016810 * q^58 - 14538456 * q^59 - 59492037 * q^60 - 74053854 * q^61 - 62432088 * q^62 - 6740532 * q^63 - 3998490 * q^64 + 515472 * q^65 + 19743711 * q^66 + 49535078 * q^67 + 42044136 * q^68 + 16181187 * q^69 + 31715142 * q^70 - 13540800 * q^71 - 10736409 * q^72 - 10485128 * q^73 - 24273480 * q^74 + 20483262 * q^75 - 1969706 * q^76 + 436896 * q^77 + 13235037 * q^78 - 12675646 * q^79 + 82500942 * q^80 - 55931040 * q^81 - 134616240 * q^82 - 109370028 * q^83 - 162354798 * q^84 - 21347802 * q^85 - 6274530 * q^86 + 39242937 * q^87 + 297723516 * q^88 + 129526410 * q^89 + 294351840 * q^90 + 106157542 * q^91 + 81571182 * q^92 + 57483711 * q^93 - 69576588 * q^94 - 118282764 * q^95 - 143765976 * q^96 - 92840294 * q^97 - 454034766 * q^98 - 158898672 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.8.a	\(\chi_{147}(1, \cdot)\)	147.8.a.a	1	1
		147.8.a.b	1
		147.8.a.c	2
		147.8.a.d	2
		147.8.a.e	3
		147.8.a.f	4
		147.8.a.g	4
		147.8.a.h	4
		147.8.a.i	4
		147.8.a.j	5
		147.8.a.k	5
		147.8.a.l	6
		147.8.a.m	6
147.8.c	\(\chi_{147}(146, \cdot)\)	147.8.c.a	2	1
		147.8.c.b	32
		147.8.c.c	56
147.8.e	\(\chi_{147}(67, \cdot)\)	147.8.e.a	2	2
		147.8.e.b	2
		147.8.e.c	2
		147.8.e.d	2
		147.8.e.e	4
		147.8.e.f	4
		147.8.e.g	4
		147.8.e.h	4
		147.8.e.i	6
		147.8.e.j	6
		147.8.e.k	8
		147.8.e.l	8
		147.8.e.m	8
		147.8.e.n	10
		147.8.e.o	12
		147.8.e.p	12
147.8.g	\(\chi_{147}(68, \cdot)\)	n/a	178	2
147.8.i	\(\chi_{147}(22, \cdot)\)	n/a	396	6
147.8.k	\(\chi_{147}(20, \cdot)\)	n/a	768	6
147.8.m	\(\chi_{147}(4, \cdot)\)	n/a	780	12
147.8.o	\(\chi_{147}(5, \cdot)\)	n/a	1548	12

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 1}\)