Space of modular forms of level 150 and weight 4

• Label: 150.4
• Level: 150
• Weight: 4
• Dimension: 415
• Nonzero newspaces: 6
• Newform subspaces: 25
• Sturm bound: 4800
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(4800\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(150))\).

	Total	New	Old
Modular forms	1912	415	1497
Cusp forms	1688	415	1273
Eisenstein series	224	0	224

Trace form

415 * q + 6 * q^2 - 19 * q^3 - 12 * q^4 - 10 * q^5 - 10 * q^6 - 32 * q^7 + 24 * q^8 - 27 * q^9 + 52 * q^10 - 100 * q^11 + 52 * q^12 + 190 * q^13 + 32 * q^14 + 256 * q^15 + 208 * q^16 - 758 * q^17 - 94 * q^18 - 572 * q^19 + 32 * q^20 - 784 * q^21 + 840 * q^22 + 1112 * q^23 + 312 * q^24 + 2774 * q^25 + 532 * q^26 + 1349 * q^27 + 352 * q^28 + 662 * q^29 - 360 * q^30 - 1080 * q^31 - 224 * q^32 - 2740 * q^33 - 3608 * q^34 - 3568 * q^35 - 1132 * q^36 - 2968 * q^37 - 744 * q^38 - 2554 * q^39 + 144 * q^40 - 294 * q^41 + 2464 * q^42 + 6012 * q^43 + 1840 * q^44 + 3630 * q^45 + 3824 * q^46 + 4016 * q^47 + 208 * q^48 + 2607 * q^49 - 252 * q^50 + 1342 * q^51 - 1160 * q^52 + 2448 * q^53 - 378 * q^54 - 344 * q^55 + 256 * q^56 - 2700 * q^57 - 5196 * q^58 - 4580 * q^59 + 1632 * q^60 - 2826 * q^61 - 2544 * q^62 - 2128 * q^63 - 192 * q^64 - 3146 * q^65 - 688 * q^66 - 1964 * q^67 + 2088 * q^68 - 3880 * q^69 + 2688 * q^70 + 1080 * q^71 + 88 * q^72 - 1550 * q^73 + 1364 * q^74 - 11256 * q^75 + 1168 * q^76 + 4032 * q^77 + 844 * q^78 + 5704 * q^79 - 160 * q^80 + 5181 * q^81 - 2436 * q^82 - 3140 * q^83 - 192 * q^84 - 4186 * q^85 - 3224 * q^86 - 2346 * q^87 - 2400 * q^88 - 5356 * q^89 + 4684 * q^90 - 1552 * q^91 - 2592 * q^92 + 5440 * q^93 - 5440 * q^94 + 7376 * q^95 + 352 * q^96 + 18130 * q^97 + 3510 * q^98 + 4140 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.4.a	\(\chi_{150}(1, \cdot)\)	150.4.a.a	1	1
		150.4.a.b	1
		150.4.a.c	1
		150.4.a.d	1
		150.4.a.e	1
		150.4.a.f	1
		150.4.a.g	1
		150.4.a.h	1
		150.4.a.i	1
150.4.c	\(\chi_{150}(49, \cdot)\)	150.4.c.a	2	1
		150.4.c.b	2
		150.4.c.c	2
		150.4.c.d	2
		150.4.c.e	2
150.4.e	\(\chi_{150}(107, \cdot)\)	150.4.e.a	4	2
		150.4.e.b	4
		150.4.e.c	12
		150.4.e.d	16
150.4.g	\(\chi_{150}(31, \cdot)\)	150.4.g.a	12	4
		150.4.g.b	16
		150.4.g.c	16
		150.4.g.d	20
150.4.h	\(\chi_{150}(19, \cdot)\)	150.4.h.a	24	4
		150.4.h.b	32
150.4.l	\(\chi_{150}(17, \cdot)\)	150.4.l.a	240	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

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