Space of modular forms of level 30 and weight 8

• Label: 30.8
• Level: 30
• Weight: 8
• Dimension: 40
• Nonzero newspaces: 3
• Newform subspaces: 9
• Sturm bound: 384
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	184	40	144
Cusp forms	152	40	112
Eisenstein series	32	0	32

Trace form

40 * q - 106 * q^3 + 164 * q^5 - 1360 * q^6 - 1120 * q^7 - 4000 * q^10 - 20720 * q^11 - 128 * q^12 - 672 * q^13 + 25216 * q^14 - 13318 * q^15 - 65536 * q^16 + 22728 * q^17 + 50624 * q^18 - 51504 * q^19 - 10496 * q^20 - 166072 * q^21 - 105664 * q^22 - 43368 * q^23 + 27648 * q^24 + 427640 * q^25 + 354816 * q^26 + 173606 * q^27 - 71680 * q^28 - 893976 * q^29 - 433776 * q^30 - 174320 * q^31 + 1336904 * q^33 + 917376 * q^34 + 230224 * q^35 + 610304 * q^36 + 106608 * q^37 - 1025088 * q^38 + 205308 * q^39 + 313344 * q^40 + 739768 * q^41 - 268928 * q^42 + 34752 * q^43 + 1038848 * q^44 - 776204 * q^45 - 2012288 * q^46 - 2645904 * q^47 - 8192 * q^48 - 1866408 * q^49 - 1216576 * q^50 + 4813756 * q^51 + 2752512 * q^52 + 3053904 * q^53 + 314928 * q^54 - 6239088 * q^55 + 462848 * q^56 - 8336080 * q^57 - 3923072 * q^58 - 6458360 * q^59 - 1924480 * q^60 - 2096448 * q^61 - 589632 * q^62 + 4216640 * q^63 + 8103168 * q^65 + 9985856 * q^66 + 27401456 * q^67 + 1454592 * q^68 + 2636496 * q^69 - 9077760 * q^70 - 4843680 * q^71 - 3239936 * q^72 - 7535432 * q^73 - 5910080 * q^74 - 25735586 * q^75 - 444416 * q^76 - 1533408 * q^77 + 4385376 * q^78 + 4759128 * q^79 + 671744 * q^80 + 39716848 * q^81 + 20843264 * q^82 + 22696608 * q^83 + 10188288 * q^84 + 20502872 * q^85 - 1329472 * q^86 - 37824052 * q^87 - 6762496 * q^88 - 24965632 * q^89 - 26446816 * q^90 - 87547776 * q^91 - 2775552 * q^92 + 50273744 * q^93 + 8846592 * q^94 - 7801896 * q^95 + 2031616 * q^96 + 85072224 * q^97 + 19273344 * q^98 + 11833128 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.8.a	\(\chi_{30}(1, \cdot)\)	30.8.a.a	1	1
		30.8.a.b	1
		30.8.a.c	1
		30.8.a.d	1
		30.8.a.e	1
		30.8.a.f	1
30.8.c	\(\chi_{30}(19, \cdot)\)	30.8.c.a	2	1
		30.8.c.b	4
30.8.e	\(\chi_{30}(17, \cdot)\)	30.8.e.a	28	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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