Space of modular forms of level 42 and weight 2

• Label: 42.2
• Level: 42
• Weight: 2
• Dimension: 13
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 192
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(42))\).

	Total	New	Old
Modular forms	72	13	59
Cusp forms	25	13	12
Eisenstein series	47	0	47

Trace form

13 * q + q^2 - q^3 - 3 * q^4 - 6 * q^5 - 5 * q^6 - 9 * q^7 + q^8 - 7 * q^9 - 6 * q^10 - 12 * q^11 - q^12 - 2 * q^13 + 7 * q^14 + 6 * q^15 + q^16 + 6 * q^17 + 13 * q^18 + 4 * q^19 + 6 * q^20 + 17 * q^21 + 12 * q^22 + 12 * q^23 + 7 * q^24 + 7 * q^25 + 2 * q^26 - q^27 - 5 * q^28 + 6 * q^29 - 6 * q^30 - 8 * q^31 + q^32 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 7 * q^36 - 18 * q^37 - 16 * q^38 - 14 * q^39 - 6 * q^40 - 6 * q^41 - 23 * q^42 - 36 * q^43 - 12 * q^44 - 6 * q^45 - 24 * q^46 + 12 * q^47 - q^48 + q^49 - 17 * q^50 + 30 * q^51 + 22 * q^52 + 18 * q^53 + 19 * q^54 + 36 * q^55 - 5 * q^56 - 8 * q^57 + 42 * q^58 + 12 * q^59 + 18 * q^60 + 22 * q^61 + 8 * q^62 + 23 * q^63 - 3 * q^64 + 12 * q^66 + 44 * q^67 + 6 * q^68 + 42 * q^70 - 11 * q^72 + 22 * q^73 + 2 * q^74 - 7 * q^75 + 4 * q^76 - 24 * q^77 - 10 * q^78 - 40 * q^79 - 6 * q^80 - 55 * q^81 - 30 * q^82 - 36 * q^83 - 19 * q^84 - 84 * q^85 - 16 * q^86 - 30 * q^87 - 6 * q^89 - 6 * q^90 - 14 * q^91 + 4 * q^93 - 24 * q^94 + 12 * q^95 + 7 * q^96 - 2 * q^97 + 25 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)

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
42.2.a	\(\chi_{42}(1, \cdot)\)	42.2.a.a	1	1
42.2.d	\(\chi_{42}(41, \cdot)\)	42.2.d.a	4	1
42.2.e	\(\chi_{42}(25, \cdot)\)	42.2.e.a	2	2
		42.2.e.b	2
42.2.f	\(\chi_{42}(5, \cdot)\)	42.2.f.a	4	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(42))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(42)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 1}\)