Space of modular forms of level 150 and weight 5

• Label: 150.5
• Level: 150
• Weight: 5
• Dimension: 554
• Nonzero newspaces: 6
• Newform subspaces: 18
• Sturm bound: 6000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(6000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(150))\).

	Total	New	Old
Modular forms	2512	554	1958
Cusp forms	2288	554	1734
Eisenstein series	224	0	224

Trace form

554 * q + 34 * q^3 - 16 * q^4 - 120 * q^5 - 80 * q^6 + 132 * q^7 + 434 * q^9 + 192 * q^10 - 576 * q^11 - 272 * q^12 - 940 * q^13 + 716 * q^15 - 896 * q^16 + 3720 * q^17 + 992 * q^18 - 3836 * q^19 - 768 * q^20 - 932 * q^21 - 3168 * q^22 - 4080 * q^23 - 384 * q^24 + 2304 * q^25 - 1536 * q^26 + 322 * q^27 + 5344 * q^28 + 13200 * q^29 + 6720 * q^30 + 5060 * q^31 + 8424 * q^33 - 6912 * q^34 - 19608 * q^35 - 5136 * q^36 - 6172 * q^37 - 7680 * q^38 - 19740 * q^39 - 1536 * q^40 - 9888 * q^41 - 13472 * q^42 - 32764 * q^43 - 13720 * q^45 + 23488 * q^46 + 22080 * q^47 + 2176 * q^48 + 43590 * q^49 + 2688 * q^50 + 7808 * q^51 + 7520 * q^52 + 24240 * q^53 + 1680 * q^54 + 18656 * q^55 + 6144 * q^56 + 3028 * q^57 - 13600 * q^58 + 14400 * q^59 - 17728 * q^60 - 2556 * q^61 - 3840 * q^62 - 8096 * q^63 - 1024 * q^64 - 13536 * q^65 - 1376 * q^66 + 5508 * q^67 + 3840 * q^68 + 28236 * q^69 - 12672 * q^70 - 40896 * q^71 - 7936 * q^72 - 15020 * q^73 - 25516 * q^75 + 4192 * q^76 - 10080 * q^77 - 20320 * q^78 - 2764 * q^79 + 7680 * q^80 + 18434 * q^81 + 27328 * q^82 + 79680 * q^83 - 6912 * q^84 + 29184 * q^85 + 16896 * q^86 + 50140 * q^87 - 25856 * q^88 - 7800 * q^89 + 73344 * q^90 - 92472 * q^91 - 3840 * q^92 - 28808 * q^93 - 46720 * q^94 - 100704 * q^95 - 5120 * q^96 - 34476 * q^97 - 76800 * q^98 - 20224 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.5.b	\(\chi_{150}(149, \cdot)\)	150.5.b.a	4	1
		150.5.b.b	8
		150.5.b.c	12
150.5.d	\(\chi_{150}(101, \cdot)\)	150.5.d.a	2	1
		150.5.d.b	4
		150.5.d.c	6
		150.5.d.d	6
		150.5.d.e	8
150.5.f	\(\chi_{150}(7, \cdot)\)	150.5.f.a	4	2
		150.5.f.b	4
		150.5.f.c	4
		150.5.f.d	4
		150.5.f.e	4
		150.5.f.f	4
150.5.i	\(\chi_{150}(29, \cdot)\)	150.5.i.a	160	4
150.5.j	\(\chi_{150}(11, \cdot)\)	150.5.j.a	160	4
150.5.k	\(\chi_{150}(13, \cdot)\)	150.5.k.a	80	8
		150.5.k.b	80

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

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