Space of modular forms of level 150 and weight 3

• Label: 150.3
• Level: 150
• Weight: 3
• Dimension: 276
• Nonzero newspaces: 6
• Newform subspaces: 13
• Sturm bound: 3600
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(3600\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(150))\).

	Total	New	Old
Modular forms	1312	276	1036
Cusp forms	1088	276	812
Eisenstein series	224	0	224

Trace form

276 * q - 8 * q^2 - 8 * q^3 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 80 * q^9 + 12 * q^10 + 32 * q^11 + 16 * q^12 + 56 * q^13 - 4 * q^15 - 32 * q^16 + 192 * q^17 - 28 * q^18 + 240 * q^19 + 32 * q^20 - 8 * q^21 + 96 * q^22 + 112 * q^23 - 156 * q^25 - 128 * q^26 - 56 * q^27 - 192 * q^28 - 400 * q^29 - 240 * q^30 - 208 * q^31 - 48 * q^32 - 312 * q^33 - 180 * q^34 - 328 * q^35 + 48 * q^36 + 512 * q^37 + 128 * q^38 + 480 * q^39 + 24 * q^40 + 256 * q^41 + 160 * q^42 + 272 * q^43 + 380 * q^45 - 160 * q^46 - 32 * q^47 - 32 * q^48 - 480 * q^49 - 92 * q^50 - 424 * q^51 - 208 * q^52 - 560 * q^53 - 480 * q^54 - 944 * q^55 - 128 * q^56 - 1040 * q^57 - 128 * q^58 - 800 * q^59 - 208 * q^60 - 32 * q^61 + 160 * q^62 - 1052 * q^63 + 44 * q^65 + 160 * q^66 + 688 * q^67 + 176 * q^68 - 300 * q^69 + 48 * q^70 - 128 * q^71 + 80 * q^72 - 24 * q^73 + 404 * q^75 + 192 * q^76 + 256 * q^77 + 128 * q^78 + 800 * q^79 + 200 * q^81 - 448 * q^82 + 256 * q^83 + 120 * q^84 + 744 * q^85 - 192 * q^86 + 1396 * q^87 + 128 * q^88 + 100 * q^89 + 924 * q^90 + 224 * q^91 + 64 * q^92 + 748 * q^93 + 640 * q^94 + 256 * q^95 + 64 * q^96 - 776 * q^97 + 248 * q^98 - 160 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.3.b	\(\chi_{150}(149, \cdot)\)	150.3.b.a	4	1
		150.3.b.b	8
150.3.d	\(\chi_{150}(101, \cdot)\)	150.3.d.a	2	1
		150.3.d.b	2
		150.3.d.c	4
		150.3.d.d	4
150.3.f	\(\chi_{150}(7, \cdot)\)	150.3.f.a	4	2
		150.3.f.b	4
		150.3.f.c	4
150.3.i	\(\chi_{150}(29, \cdot)\)	150.3.i.a	80	4
150.3.j	\(\chi_{150}(11, \cdot)\)	150.3.j.a	80	4
150.3.k	\(\chi_{150}(13, \cdot)\)	150.3.k.a	32	8
		150.3.k.b	48

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)