Space of modular forms of level 150 and weight 12

• Label: 150.12
• Level: 150
• Weight: 12
• Dimension: 1521
• Nonzero newspaces: 6
• Sturm bound: 14400
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(14400\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(150))\).

	Total	New	Old
Modular forms	6712	1521	5191
Cusp forms	6488	1521	4967
Eisenstein series	224	0	224

Trace form

1521 * q + 96 * q^2 + 2267 * q^3 - 1024 * q^4 + 7310 * q^5 + 13664 * q^6 - 125504 * q^7 + 98304 * q^8 - 59049 * q^9 - 244928 * q^10 + 933860 * q^11 - 1823744 * q^12 - 8063382 * q^13 + 335360 * q^14 + 2525836 * q^15 + 49283072 * q^16 + 34069030 * q^17 + 8523296 * q^18 + 99107372 * q^19 + 10821632 * q^20 - 84924712 * q^21 - 174500736 * q^22 + 123928664 * q^23 + 103514112 * q^24 + 235042814 * q^25 + 103826752 * q^26 + 129536243 * q^27 - 451158016 * q^28 - 102885742 * q^29 + 1102442880 * q^30 + 1011817208 * q^31 - 234881024 * q^32 - 3450085924 * q^33 + 33255040 * q^34 + 3104300312 * q^35 - 2328060928 * q^36 + 3214247812 * q^37 + 1435337088 * q^38 - 4863329590 * q^39 - 597098496 * q^40 - 3226039314 * q^41 - 3885312512 * q^42 + 11700408692 * q^43 + 6286594048 * q^44 - 8201390970 * q^45 - 11431233792 * q^46 - 15407423728 * q^47 - 1867513856 * q^48 + 29405618721 * q^49 + 9631637568 * q^50 + 10527526810 * q^51 + 5619689472 * q^52 - 18459845508 * q^53 - 3214155168 * q^54 - 50089213944 * q^55 - 10049552384 * q^56 + 49335731052 * q^57 + 67994245952 * q^58 + 68791068580 * q^59 - 20266549248 * q^60 - 65536328382 * q^61 - 24231887616 * q^62 + 6252733724 * q^63 - 1073741824 * q^64 - 63066095666 * q^65 + 976841984 * q^66 + 130262022844 * q^67 + 17705072640 * q^68 + 84434186396 * q^69 + 25859985408 * q^70 + 46545087720 * q^71 - 16467525632 * q^72 + 30267982598 * q^73 - 141530744512 * q^74 - 281320668636 * q^75 + 33975529472 * q^76 + 178872167424 * q^77 + 184350973120 * q^78 + 70628683176 * q^79 + 7665090560 * q^80 - 59211038577 * q^81 + 3675367360 * q^82 + 58475328148 * q^83 - 387982258176 * q^84 - 719906231626 * q^85 - 40075274624 * q^86 + 838380892902 * q^87 + 129044709376 * q^88 + 558631102136 * q^89 - 60423523136 * q^90 + 333377689328 * q^91 - 90182344704 * q^92 + 114864850060 * q^93 - 862407093248 * q^94 - 453869439664 * q^95 + 1979711488 * q^96 - 680160138410 * q^97 + 835989873504 * q^98 + 362516691348 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.12.a	\(\chi_{150}(1, \cdot)\)	150.12.a.a	1	1
		150.12.a.b	1
		150.12.a.c	1
		150.12.a.d	1
		150.12.a.e	1
		150.12.a.f	1
		150.12.a.g	1
		150.12.a.h	1
		150.12.a.i	1
		150.12.a.j	2
		150.12.a.k	2
		150.12.a.l	2
		150.12.a.m	2
		150.12.a.n	2
		150.12.a.o	2
		150.12.a.p	2
		150.12.a.q	2
		150.12.a.r	2
		150.12.a.s	2
		150.12.a.t	3
		150.12.a.u	3
150.12.c	\(\chi_{150}(49, \cdot)\)	150.12.c.a	2	1
		150.12.c.b	2
		150.12.c.c	2
		150.12.c.d	2
		150.12.c.e	2
		150.12.c.f	2
		150.12.c.g	2
		150.12.c.h	2
		150.12.c.i	2
		150.12.c.j	4
		150.12.c.k	4
		150.12.c.l	4
		150.12.c.m	4
150.12.e	\(\chi_{150}(107, \cdot)\)	n/a	132	2
150.12.g	\(\chi_{150}(31, \cdot)\)	n/a	224	4
150.12.h	\(\chi_{150}(19, \cdot)\)	n/a	216	4
150.12.l	\(\chi_{150}(17, \cdot)\)	n/a	880	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

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