Space of modular forms of level 30 and weight 2

• Label: 30.2
• Level: 30
• Weight: 2
• Dimension: 7
• Nonzero newspaces: 3
• Newform subspaces: 3
• Sturm bound: 96
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(30))\).

	Total	New	Old
Modular forms	40	7	33
Cusp forms	9	7	2
Eisenstein series	31	0	31

Trace form

7 * q - q^2 - 3 * q^3 - q^4 - 5 * q^5 - 3 * q^6 - 8 * q^7 - q^8 - q^9 + 3 * q^10 + 4 * q^11 + 5 * q^12 + 2 * q^13 + 8 * q^14 + 9 * q^15 - q^16 + 6 * q^17 + 7 * q^18 - 4 * q^19 + 3 * q^20 - 4 * q^22 - 3 * q^24 - 9 * q^25 - 14 * q^26 - 3 * q^27 - 8 * q^28 - 6 * q^29 - 15 * q^30 - 16 * q^31 - q^32 - 4 * q^33 - 2 * q^34 + 8 * q^35 - q^36 + 26 * q^37 + 4 * q^38 + 14 * q^39 + 11 * q^40 - 2 * q^41 + 8 * q^42 + 20 * q^43 - 4 * q^44 - 5 * q^45 + 24 * q^46 + 5 * q^48 + 15 * q^49 + 7 * q^50 - 6 * q^51 + 2 * q^52 - 6 * q^53 - 3 * q^54 + 4 * q^55 - 20 * q^57 - 14 * q^58 - 20 * q^59 - 7 * q^60 - 30 * q^61 - 8 * q^62 - 8 * q^63 - q^64 - 14 * q^65 + 12 * q^66 - 20 * q^67 + 6 * q^68 - 8 * q^69 - 8 * q^70 + 24 * q^71 - 9 * q^72 - 18 * q^73 + 2 * q^74 + 21 * q^75 + 12 * q^76 - 2 * q^78 + 8 * q^79 - 5 * q^80 + 31 * q^81 - 10 * q^82 + 12 * q^83 + 6 * q^85 + 12 * q^86 + 14 * q^87 - 4 * q^88 + 38 * q^89 + 11 * q^90 + 16 * q^91 + 16 * q^93 - 16 * q^94 + 4 * q^95 + 5 * q^96 + 14 * q^97 - 9 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)

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
30.2.a	\(\chi_{30}(1, \cdot)\)	30.2.a.a	1	1
30.2.c	\(\chi_{30}(19, \cdot)\)	30.2.c.a	2	1
30.2.e	\(\chi_{30}(17, \cdot)\)	30.2.e.a	4	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(30))\) into lower level spaces

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