Space of modular forms of level 30 and weight 3

• Label: 30.3
• Level: 30
• Weight: 3
• Dimension: 12
• Nonzero newspaces: 3
• Newform subspaces: 3
• Sturm bound: 144
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	64	12	52
Cusp forms	32	12	20
Eisenstein series	32	0	32

Trace form

12 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 40 * q^9 - 12 * q^10 - 16 * q^11 - 8 * q^12 - 28 * q^13 + 4 * q^15 + 16 * q^16 + 44 * q^17 + 44 * q^18 + 80 * q^19 + 8 * q^20 + 64 * q^21 + 32 * q^22 - 16 * q^23 + 36 * q^25 + 24 * q^26 + 28 * q^27 + 16 * q^28 - 176 * q^31 - 16 * q^32 - 24 * q^33 - 160 * q^34 - 112 * q^35 - 24 * q^36 - 196 * q^37 - 64 * q^38 - 40 * q^39 - 24 * q^40 + 32 * q^41 - 80 * q^42 + 104 * q^43 - 60 * q^45 + 80 * q^46 + 96 * q^47 + 16 * q^48 + 240 * q^49 + 92 * q^50 + 152 * q^51 + 104 * q^52 + 100 * q^53 + 240 * q^54 + 464 * q^55 + 64 * q^56 + 200 * q^57 + 64 * q^58 - 72 * q^60 - 224 * q^61 - 80 * q^62 - 304 * q^63 - 204 * q^65 - 320 * q^66 - 344 * q^67 - 88 * q^68 - 200 * q^69 - 48 * q^70 + 64 * q^71 - 40 * q^72 + 12 * q^73 - 244 * q^75 - 96 * q^76 - 128 * q^77 + 136 * q^78 - 400 * q^79 + 180 * q^81 + 224 * q^82 + 192 * q^83 + 240 * q^84 - 44 * q^85 + 96 * q^86 + 192 * q^87 - 64 * q^88 + 36 * q^90 + 208 * q^91 - 32 * q^92 - 64 * q^93 - 320 * q^94 + 64 * q^95 - 32 * q^96 + 428 * q^97 - 124 * q^98 + 80 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)

We only show spaces with odd 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
30.3.b	\(\chi_{30}(29, \cdot)\)	30.3.b.a	4	1
30.3.d	\(\chi_{30}(11, \cdot)\)	30.3.d.a	4	1
30.3.f	\(\chi_{30}(7, \cdot)\)	30.3.f.a	4	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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