Space of modular forms of level 30 and weight 16

• Label: 30.16
• Level: 30
• Weight: 16
• Dimension: 84
• Nonzero newspaces: 3
• Newform subspaces: 12
• Sturm bound: 768
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(768\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	376	84	292
Cusp forms	344	84	260
Eisenstein series	32	0	32

Trace form

84 * q + 1502 * q^3 - 65536 * q^4 - 488416 * q^5 + 666368 * q^6 - 577096 * q^7 - 19131876 * q^9 + 27338240 * q^10 - 128915168 * q^11 + 118718464 * q^12 - 1222650568 * q^13 + 1100154880 * q^14 + 225278522 * q^15 - 9663676416 * q^16 + 3753707832 * q^17 - 2617271296 * q^18 - 12114130192 * q^19 + 8002207744 * q^20 - 11776770544 * q^21 + 1703605248 * q^22 + 1322221608 * q^23 + 9172942848 * q^24 + 8223371380 * q^25 - 133752471552 * q^26 + 214197641798 * q^27 - 9455140864 * q^28 - 112953806928 * q^29 + 98214422784 * q^30 + 8412977536 * q^31 - 585213440368 * q^33 + 507899115520 * q^34 + 1505869596784 * q^35 + 1387818450944 * q^36 - 368094509272 * q^37 + 1267276889088 * q^38 - 1458501945660 * q^39 - 699333083136 * q^40 - 4927163265056 * q^41 - 2594788960256 * q^42 - 2088800834488 * q^43 + 5753937723392 * q^44 - 4175540536784 * q^45 - 8951287638016 * q^46 - 12763021216176 * q^47 + 1945083314176 * q^48 + 27218894090244 * q^49 + 3431478631424 * q^50 - 13345180401524 * q^51 - 11964652060672 * q^52 + 13082586577776 * q^53 + 2677850419968 * q^54 + 8841670630432 * q^55 + 8724571750400 * q^56 + 93716491978616 * q^57 - 53458304821248 * q^58 - 51532097815640 * q^59 - 2575322152960 * q^60 - 22859616858408 * q^61 + 91158908931072 * q^62 - 25411783961584 * q^63 - 17592186044416 * q^64 - 74674455456672 * q^65 - 126249227619328 * q^66 - 18499569160600 * q^67 + 61500749119488 * q^68 + 80953388457984 * q^69 + 73774105067520 * q^70 + 269775723812832 * q^71 + 42881372913664 * q^72 - 444655339675648 * q^73 - 240535681123328 * q^74 - 408481548827306 * q^75 + 22080451248128 * q^76 + 560050217032608 * q^77 + 283227896108544 * q^78 - 524880253979656 * q^79 - 131108171677696 * q^80 + 261329585750284 * q^81 - 640990951968768 * q^82 - 947454062414688 * q^83 + 109114735067136 * q^84 + 1526505990956992 * q^85 + 1333370325380096 * q^86 + 459119566476092 * q^87 + 27911868383232 * q^88 - 1689387072986776 * q^89 - 1416851034021376 * q^90 + 2589439716065968 * q^91 + 21663278825472 * q^92 + 5395864555575584 * q^93 + 830421035552768 * q^94 + 1276597056174504 * q^95 - 479455789187072 * q^96 - 9696820160610856 * q^97 - 1449387426945024 * q^98 + 1679742783136872 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.16.a	\(\chi_{30}(1, \cdot)\)	30.16.a.a	1	1
		30.16.a.b	1
		30.16.a.c	1
		30.16.a.d	1
		30.16.a.e	1
		30.16.a.f	1
		30.16.a.g	2
		30.16.a.h	2
30.16.c	\(\chi_{30}(19, \cdot)\)	30.16.c.a	2	1
		30.16.c.b	4
		30.16.c.c	8
30.16.e	\(\chi_{30}(17, \cdot)\)	30.16.e.a	60	2

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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