Space of modular forms of level 150 and weight 16

• Label: 150.16
• Level: 150
• Weight: 16
• Dimension: 2073
• Nonzero newspaces: 6
• Sturm bound: 19200
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(19200\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(150))\).

	Total	New	Old
Modular forms	9112	2073	7039
Cusp forms	8888	2073	6815
Eisenstein series	224	0	224

Trace form

2073 * q - 384 * q^2 + 3557 * q^3 - 16384 * q^4 + 840070 * q^5 - 2172544 * q^6 + 1896296 * q^7 - 6291456 * q^8 - 4782969 * q^9 - 62835968 * q^10 + 93386764 * q^11 - 129941504 * q^12 + 1734864698 * q^13 - 550077440 * q^14 - 1333969424 * q^15 + 16911433728 * q^16 - 22436697490 * q^17 + 9520082816 * q^18 - 63682648588 * q^19 + 8962834432 * q^20 + 33711001352 * q^21 - 143352423936 * q^22 - 44186607896 * q^23 + 59624128512 * q^24 + 106994238734 * q^25 - 102688908544 * q^26 - 397014223987 * q^27 + 551020396544 * q^28 + 263014629898 * q^29 - 843069811200 * q^30 - 416657462288 * q^31 + 240518168576 * q^32 + 2530481021396 * q^33 - 5864120046080 * q^34 + 2805015486352 * q^35 - 3480914378752 * q^36 - 2323025917548 * q^37 - 1334826803712 * q^38 + 2654419607990 * q^39 + 117738307584 * q^40 + 6300105866718 * q^41 + 300477764608 * q^42 + 21888420712972 * q^43 - 14202118930432 * q^44 + 522036847830 * q^45 + 17225608107008 * q^46 - 25473581157728 * q^47 - 2128961601536 * q^48 + 7660298487201 * q^49 + 14581817872128 * q^50 + 13597435829902 * q^51 + 12289513521152 * q^52 - 120138918811308 * q^53 - 9372476469888 * q^54 + 143316782104456 * q^55 + 9588262830080 * q^56 - 194089598126868 * q^57 + 46755361865472 * q^58 - 60267086987140 * q^59 + 29724596109312 * q^60 + 24389189721874 * q^61 + 10557903058944 * q^62 - 496419777776776 * q^63 - 4398046511104 * q^64 - 320031782072626 * q^65 - 16748799809536 * q^66 + 230285453680244 * q^67 + 78820851548160 * q^68 + 74040562621976 * q^69 - 207460933650432 * q^70 - 599040159023736 * q^71 - 115854584840192 * q^72 + 1553931866096438 * q^73 + 920737163469568 * q^74 - 878244018035976 * q^75 - 103245900611584 * q^76 - 2841468157384416 * q^77 + 790052206048000 * q^78 + 2292222362626256 * q^79 + 225504573521920 * q^80 - 2631084228472017 * q^81 + 1213553772099840 * q^82 - 1352247569424532 * q^83 + 1109186594340864 * q^84 + 527151088702454 * q^85 - 1475026280816128 * q^86 - 4387038137978898 * q^87 + 986642714198016 * q^88 + 2840746615773616 * q^89 + 5472334742427904 * q^90 - 2664983663433824 * q^91 - 742311461781504 * q^92 - 7653056811110840 * q^93 - 2546345915619328 * q^94 - 5275304498294384 * q^95 + 733477334941696 * q^96 + 20926209980192390 * q^97 + 2537527093305984 * q^98 - 4146014073399012 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.16.a	\(\chi_{150}(1, \cdot)\)	150.16.a.a	1	1
		150.16.a.b	1
		150.16.a.c	1
		150.16.a.d	1
		150.16.a.e	1
		150.16.a.f	1
		150.16.a.g	1
		150.16.a.h	1
		150.16.a.i	1
		150.16.a.j	1
		150.16.a.k	1
		150.16.a.l	2
		150.16.a.m	2
		150.16.a.n	2
		150.16.a.o	2
		150.16.a.p	2
		150.16.a.q	2
		150.16.a.r	2
		150.16.a.s	2
		150.16.a.t	3
		150.16.a.u	3
		150.16.a.v	3
		150.16.a.w	3
		150.16.a.x	4
		150.16.a.y	4
150.16.c	\(\chi_{150}(49, \cdot)\)	150.16.c.a	2	1
		150.16.c.b	2
		150.16.c.c	2
		150.16.c.d	2
		150.16.c.e	2
		150.16.c.f	2
		150.16.c.g	2
		150.16.c.h	2
		150.16.c.i	2
		150.16.c.j	4
		150.16.c.k	4
		150.16.c.l	4
		150.16.c.m	4
		150.16.c.n	6
		150.16.c.o	6
150.16.e	\(\chi_{150}(107, \cdot)\)	n/a	180	2
150.16.g	\(\chi_{150}(31, \cdot)\)	n/a	304	4
150.16.h	\(\chi_{150}(19, \cdot)\)	n/a	296	4
150.16.l	\(\chi_{150}(17, \cdot)\)	n/a	1200	8

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)