Space of modular forms of level 147 and weight 3

• Label: 147.3
• Level: 147
• Weight: 3
• Dimension: 1080
• Nonzero newspaces: 8
• Newform subspaces: 30
• Sturm bound: 4704
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(4704\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(147))\).

	Total	New	Old
Modular forms	1688	1178	510
Cusp forms	1448	1080	368
Eisenstein series	240	98	142

Trace form

1080 * q - 9 * q^3 + 2 * q^4 + 12 * q^5 - 9 * q^6 - 44 * q^7 + 12 * q^8 + 27 * q^9 - 18 * q^10 - 12 * q^11 - 57 * q^12 - 46 * q^13 - 24 * q^14 - 135 * q^15 - 222 * q^16 - 96 * q^17 - 213 * q^18 - 46 * q^19 + 3 * q^21 + 138 * q^22 + 192 * q^23 + 279 * q^24 + 222 * q^25 + 252 * q^26 + 243 * q^27 + 60 * q^28 + 24 * q^29 - 69 * q^30 - 214 * q^31 - 156 * q^32 - 393 * q^33 - 522 * q^34 - 210 * q^35 - 435 * q^36 - 978 * q^37 - 1188 * q^38 - 594 * q^39 - 2250 * q^40 - 588 * q^41 - 453 * q^42 - 122 * q^43 - 672 * q^44 + 249 * q^45 - 138 * q^46 + 360 * q^47 + 378 * q^48 + 246 * q^49 + 564 * q^50 + 567 * q^51 + 886 * q^52 + 444 * q^53 + 147 * q^54 + 1116 * q^55 + 1998 * q^56 + 123 * q^57 + 1638 * q^58 + 756 * q^59 + 1299 * q^60 + 1156 * q^61 + 1176 * q^62 + 6 * q^63 + 1142 * q^64 - 36 * q^65 + 51 * q^66 - 246 * q^67 - 72 * q^68 - 597 * q^69 + 18 * q^70 - 240 * q^71 - 369 * q^72 + 158 * q^73 - 180 * q^74 - 381 * q^75 + 542 * q^76 - 72 * q^77 - 735 * q^78 - 366 * q^79 - 2238 * q^80 - 1365 * q^81 - 3408 * q^82 - 2352 * q^83 - 3126 * q^84 - 1758 * q^85 - 3654 * q^86 - 1725 * q^87 - 4152 * q^88 - 1224 * q^89 - 2550 * q^90 - 902 * q^91 - 1302 * q^92 - 501 * q^93 - 528 * q^94 + 204 * q^95 + 510 * q^96 + 668 * q^97 + 858 * q^98 + 1140 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.3.b	\(\chi_{147}(50, \cdot)\)	147.3.b.a	1	1
		147.3.b.b	1
		147.3.b.c	2
		147.3.b.d	2
		147.3.b.e	4
		147.3.b.f	4
		147.3.b.g	8
147.3.d	\(\chi_{147}(97, \cdot)\)	147.3.d.a	2	1
		147.3.d.b	2
		147.3.d.c	2
		147.3.d.d	8
147.3.f	\(\chi_{147}(19, \cdot)\)	147.3.f.a	2	2
		147.3.f.b	2
		147.3.f.c	2
		147.3.f.d	2
		147.3.f.e	2
		147.3.f.f	8
		147.3.f.g	8
147.3.h	\(\chi_{147}(116, \cdot)\)	147.3.h.a	2	2
		147.3.h.b	4
		147.3.h.c	8
		147.3.h.d	8
		147.3.h.e	8
		147.3.h.f	16
147.3.j	\(\chi_{147}(13, \cdot)\)	147.3.j.a	108	6
147.3.l	\(\chi_{147}(8, \cdot)\)	147.3.l.a	216	6
147.3.n	\(\chi_{147}(2, \cdot)\)	147.3.n.a	12	12
		147.3.n.b	408
147.3.p	\(\chi_{147}(10, \cdot)\)	147.3.p.a	108	12
		147.3.p.b	120

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

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