Space of modular forms of level 147 and weight 2

• Label: 147.2
• Level: 147
• Weight: 2
• Dimension: 517
• Nonzero newspaces: 8
• Newform subspaces: 21
• Sturm bound: 3136
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(3136\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(147))\).

	Total	New	Old
Modular forms	904	613	291
Cusp forms	665	517	148
Eisenstein series	239	96	143

Trace form

517 * q + 3 * q^2 - 16 * q^3 - 39 * q^4 - 6 * q^5 - 30 * q^6 - 44 * q^7 - 21 * q^8 - 28 * q^9 - 72 * q^10 - 24 * q^11 - 34 * q^12 - 56 * q^13 - 24 * q^14 - 33 * q^15 - 71 * q^16 - 6 * q^17 - 18 * q^18 - 50 * q^19 - 30 * q^20 - 25 * q^21 - 90 * q^22 - 24 * q^23 - 42 * q^24 - 83 * q^25 - 42 * q^26 - 28 * q^27 - 108 * q^28 - 42 * q^29 - 51 * q^30 - 86 * q^31 - 69 * q^32 - 45 * q^33 - 108 * q^34 - 42 * q^35 - 28 * q^36 - 28 * q^37 + 36 * q^38 + 14 * q^39 + 132 * q^40 + 78 * q^41 + 51 * q^42 - 30 * q^43 + 168 * q^44 + 15 * q^45 + 138 * q^46 + 24 * q^47 + 141 * q^48 + 78 * q^49 + 81 * q^50 + 57 * q^51 + 180 * q^52 + 42 * q^53 - 18 * q^54 + 96 * q^55 + 150 * q^56 - 65 * q^57 + 48 * q^58 - 24 * q^59 + 51 * q^60 - 6 * q^61 - 84 * q^62 - 36 * q^63 - 75 * q^64 - 96 * q^65 - 57 * q^66 - 106 * q^67 - 138 * q^68 - 45 * q^69 - 150 * q^70 - 48 * q^71 - 42 * q^72 - 56 * q^73 - 90 * q^74 - 22 * q^75 - 182 * q^76 - 72 * q^77 + 15 * q^78 - 118 * q^79 - 48 * q^80 + 80 * q^81 + 6 * q^82 + 84 * q^83 + 164 * q^84 - 42 * q^85 + 174 * q^86 + 129 * q^87 + 216 * q^88 + 138 * q^89 + 372 * q^90 + 22 * q^91 + 126 * q^92 + 247 * q^93 + 168 * q^94 + 228 * q^95 + 225 * q^96 + 58 * q^97 + 438 * q^98 + 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.2.a	\(\chi_{147}(1, \cdot)\)	147.2.a.a	1	1
		147.2.a.b	1
		147.2.a.c	1
		147.2.a.d	2
		147.2.a.e	2
147.2.c	\(\chi_{147}(146, \cdot)\)	147.2.c.a	2	1
		147.2.c.b	8
147.2.e	\(\chi_{147}(67, \cdot)\)	147.2.e.a	2	2
		147.2.e.b	2
		147.2.e.c	2
		147.2.e.d	4
		147.2.e.e	4
147.2.g	\(\chi_{147}(68, \cdot)\)	147.2.g.a	2	2
		147.2.g.b	16
147.2.i	\(\chi_{147}(22, \cdot)\)	147.2.i.a	24	6
		147.2.i.b	36
147.2.k	\(\chi_{147}(20, \cdot)\)	147.2.k.a	96	6
147.2.m	\(\chi_{147}(4, \cdot)\)	147.2.m.a	48	12
		147.2.m.b	60
147.2.o	\(\chi_{147}(5, \cdot)\)	147.2.o.a	12	12
		147.2.o.b	192

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

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