Space of modular forms of level 147 and weight 4

• Label: 147.4
• Level: 147
• Weight: 4
• Dimension: 1644
• Nonzero newspaces: 8
• Newform subspaces: 41
• Sturm bound: 6272
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 41 \)
Sturm bound:			\(6272\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(147))\).

	Total	New	Old
Modular forms	2472	1740	732
Cusp forms	2232	1644	588
Eisenstein series	240	96	144

Trace form

1644 * q - 27 * q^3 - 30 * q^4 + 48 * q^5 + 51 * q^6 + 12 * q^7 - 108 * q^8 - 99 * q^9 - 138 * q^10 + 171 * q^12 + 126 * q^13 + 312 * q^14 + 357 * q^15 + 210 * q^16 + 24 * q^17 - 561 * q^18 - 1158 * q^19 - 2088 * q^20 - 606 * q^21 - 942 * q^22 + 336 * q^23 - 309 * q^24 + 810 * q^25 + 588 * q^26 + 195 * q^27 + 1068 * q^28 + 1296 * q^29 + 3039 * q^30 + 1458 * q^31 + 2436 * q^32 + 1581 * q^33 + 510 * q^34 - 84 * q^35 - 555 * q^36 + 1818 * q^37 + 1788 * q^38 - 387 * q^39 + 3174 * q^40 + 288 * q^41 - 2847 * q^42 - 3894 * q^43 - 11424 * q^44 - 5835 * q^45 - 12042 * q^46 - 5448 * q^47 - 5280 * q^48 - 5760 * q^49 - 1212 * q^50 + 2589 * q^51 - 1770 * q^52 + 1848 * q^53 + 8295 * q^54 + 738 * q^55 + 1326 * q^56 + 1269 * q^57 - 42 * q^58 + 5880 * q^59 + 4443 * q^60 + 4266 * q^61 + 7632 * q^62 - 1170 * q^63 + 582 * q^64 - 1008 * q^65 - 1785 * q^66 - 1878 * q^67 + 3072 * q^68 + 3291 * q^69 + 3462 * q^70 + 984 * q^71 + 8079 * q^72 + 8610 * q^73 + 5460 * q^74 + 4587 * q^75 + 11046 * q^76 + 180 * q^77 + 2841 * q^78 + 978 * q^79 + 20142 * q^80 + 6705 * q^81 + 15012 * q^82 + 10584 * q^83 + 11658 * q^84 + 498 * q^85 - 42 * q^86 - 1149 * q^87 + 348 * q^88 - 696 * q^89 - 14220 * q^90 - 10086 * q^91 - 10290 * q^92 - 18159 * q^93 - 33180 * q^94 - 33264 * q^95 - 28704 * q^96 - 16896 * q^97 - 51054 * q^98 - 7128 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.4.a	\(\chi_{147}(1, \cdot)\)	147.4.a.a	1	1
		147.4.a.b	1
		147.4.a.c	1
		147.4.a.d	1
		147.4.a.e	1
		147.4.a.f	1
		147.4.a.g	1
		147.4.a.h	1
		147.4.a.i	2
		147.4.a.j	2
		147.4.a.k	2
		147.4.a.l	3
		147.4.a.m	3
147.4.c	\(\chi_{147}(146, \cdot)\)	147.4.c.a	12	1
		147.4.c.b	24
147.4.e	\(\chi_{147}(67, \cdot)\)	147.4.e.a	2	2
		147.4.e.b	2
		147.4.e.c	2
		147.4.e.d	2
		147.4.e.e	2
		147.4.e.f	2
		147.4.e.g	2
		147.4.e.h	2
		147.4.e.i	2
		147.4.e.j	4
		147.4.e.k	4
		147.4.e.l	4
		147.4.e.m	4
		147.4.e.n	6
147.4.g	\(\chi_{147}(68, \cdot)\)	147.4.g.a	2	2
		147.4.g.b	2
		147.4.g.c	8
		147.4.g.d	12
		147.4.g.e	48
147.4.i	\(\chi_{147}(22, \cdot)\)	147.4.i.a	84	6
		147.4.i.b	84
147.4.k	\(\chi_{147}(20, \cdot)\)	147.4.k.a	12	6
		147.4.k.b	312
147.4.m	\(\chi_{147}(4, \cdot)\)	147.4.m.a	156	12
		147.4.m.b	180
147.4.o	\(\chi_{147}(5, \cdot)\)	147.4.o.a	648	12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

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