Space of modular forms of level 150 and weight 2

• Label: 150.2
• Level: 150
• Weight: 2
• Dimension: 137
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 2400
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2400\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(150))\).

	Total	New	Old
Modular forms	712	137	575
Cusp forms	489	137	352
Eisenstein series	223	0	223

Trace form

137 * q + 3 * q^2 + 7 * q^3 + 3 * q^4 + 10 * q^5 + 7 * q^6 + 24 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 4 * q^11 - 9 * q^12 + 10 * q^13 - 8 * q^14 - 4 * q^15 + 3 * q^16 - 34 * q^17 - 23 * q^18 - 52 * q^19 - 8 * q^20 - 32 * q^21 - 60 * q^22 - 56 * q^23 - 13 * q^24 - 86 * q^25 + 2 * q^26 + 7 * q^27 - 16 * q^28 - 38 * q^29 - 20 * q^30 - 16 * q^31 - 7 * q^32 - 20 * q^33 - 28 * q^34 - 8 * q^35 + 3 * q^36 - 24 * q^37 + 12 * q^38 - 54 * q^39 - 6 * q^40 + 6 * q^41 - 8 * q^42 - 76 * q^43 + 20 * q^44 - 70 * q^45 - 24 * q^46 - 32 * q^47 - 9 * q^48 - 63 * q^49 + 18 * q^50 - 30 * q^51 + 10 * q^52 - 24 * q^53 + 7 * q^54 - 24 * q^55 + 8 * q^56 - 20 * q^57 + 58 * q^58 + 20 * q^59 + 32 * q^60 + 82 * q^61 + 48 * q^62 + 84 * q^63 + 3 * q^64 + 74 * q^65 + 48 * q^66 + 108 * q^67 + 6 * q^68 + 180 * q^69 + 48 * q^70 + 24 * q^71 + 19 * q^72 + 110 * q^73 + 34 * q^74 + 164 * q^75 - 4 * q^76 + 96 * q^77 + 118 * q^78 + 64 * q^79 + 10 * q^80 + 19 * q^81 + 62 * q^82 + 20 * q^83 + 68 * q^84 + 34 * q^85 + 20 * q^86 + 62 * q^87 + 20 * q^88 + 4 * q^89 + 54 * q^90 + 24 * q^92 - 20 * q^93 + 80 * q^94 + 16 * q^95 - 9 * q^96 + 30 * q^97 + 75 * q^98 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.2.a	\(\chi_{150}(1, \cdot)\)	150.2.a.a	1	1
		150.2.a.b	1
		150.2.a.c	1
150.2.c	\(\chi_{150}(49, \cdot)\)	150.2.c.a	2	1
150.2.e	\(\chi_{150}(107, \cdot)\)	150.2.e.a	4	2
		150.2.e.b	8
150.2.g	\(\chi_{150}(31, \cdot)\)	150.2.g.a	4	4
		150.2.g.b	4
		150.2.g.c	8
150.2.h	\(\chi_{150}(19, \cdot)\)	150.2.h.a	8	4
		150.2.h.b	16
150.2.l	\(\chi_{150}(17, \cdot)\)	150.2.l.a	80	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

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