Space of modular forms of level 30 and weight 4

• Label: 30.4
• Level: 30
• Weight: 4
• Dimension: 16
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 192
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	88	16	72
Cusp forms	56	16	40
Eisenstein series	32	0	32

Trace form

16 * q + 14 * q^3 + 4 * q^5 - 4 * q^6 + 40 * q^7 - 40 * q^10 + 32 * q^11 - 8 * q^12 - 152 * q^13 - 64 * q^14 - 238 * q^15 - 128 * q^16 - 72 * q^17 - 16 * q^18 + 16 * q^19 - 16 * q^20 + 560 * q^21 + 336 * q^22 + 72 * q^23 + 48 * q^24 + 320 * q^25 + 288 * q^26 - 634 * q^27 + 160 * q^28 - 216 * q^29 + 84 * q^30 - 48 * q^31 + 464 * q^33 - 224 * q^34 + 224 * q^35 + 512 * q^36 + 568 * q^37 + 432 * q^38 + 228 * q^39 - 96 * q^40 - 376 * q^41 - 1088 * q^42 - 2648 * q^43 - 992 * q^44 - 1364 * q^45 - 1408 * q^46 - 144 * q^47 - 32 * q^48 + 1032 * q^49 - 176 * q^50 + 172 * q^51 + 352 * q^52 + 144 * q^53 + 108 * q^54 + 1792 * q^55 - 320 * q^56 + 1160 * q^57 + 2688 * q^58 + 1640 * q^59 + 1160 * q^60 + 560 * q^61 + 1008 * q^62 + 1520 * q^63 + 1008 * q^65 + 176 * q^66 - 344 * q^67 - 288 * q^68 - 384 * q^69 - 2880 * q^70 - 1728 * q^71 + 64 * q^72 + 448 * q^73 + 80 * q^74 - 1226 * q^75 - 704 * q^76 - 1728 * q^77 - 3864 * q^78 - 2072 * q^79 + 64 * q^80 - 3992 * q^81 + 1344 * q^82 - 1152 * q^83 + 288 * q^84 - 608 * q^85 + 1456 * q^86 + 4268 * q^87 + 1344 * q^88 + 1408 * q^89 + 5384 * q^90 + 2768 * q^91 + 288 * q^92 + 704 * q^93 + 2432 * q^94 - 1176 * q^95 - 320 * q^96 - 8936 * q^97 - 2016 * q^98 - 2232 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.4.a	\(\chi_{30}(1, \cdot)\)	30.4.a.a	1	1
		30.4.a.b	1
30.4.c	\(\chi_{30}(19, \cdot)\)	30.4.c.a	2	1
30.4.e	\(\chi_{30}(17, \cdot)\)	30.4.e.a	12	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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