Space of modular forms of level 74 and weight 2

• Label: 74.2
• Level: 74
• Weight: 2
• Dimension: 56
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 684
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(684\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(74))\).

	Total	New	Old
Modular forms	207	56	151
Cusp forms	136	56	80
Eisenstein series	71	0	71

Trace form

56 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 6 * q^10 - 12 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 24 * q^15 - q^16 - 18 * q^17 - 13 * q^18 - 20 * q^19 - 6 * q^20 - 32 * q^21 - 12 * q^22 - 24 * q^23 - 4 * q^24 - 31 * q^25 - 5 * q^26 + 8 * q^27 + 4 * q^28 + 6 * q^29 + 48 * q^30 + 76 * q^31 - q^32 + 24 * q^33 + 54 * q^34 + 60 * q^35 + 32 * q^36 + 47 * q^37 + 16 * q^38 + 28 * q^39 + 39 * q^40 + 66 * q^41 + 40 * q^42 + 28 * q^43 - 12 * q^44 + 30 * q^45 + 48 * q^46 - 12 * q^47 + 8 * q^48 - 9 * q^49 - 22 * q^50 - 72 * q^51 - 14 * q^52 - 54 * q^53 - 40 * q^54 - 72 * q^55 - 8 * q^56 - 80 * q^57 - 30 * q^58 - 24 * q^59 - 24 * q^60 - 17 * q^61 - 32 * q^62 + 4 * q^63 - q^64 - 3 * q^65 - 48 * q^66 - 32 * q^67 - 18 * q^68 + 48 * q^69 - 48 * q^70 - 13 * q^72 - 2 * q^73 - 37 * q^74 + 56 * q^75 - 20 * q^76 - 24 * q^77 - 56 * q^78 - 8 * q^79 - 6 * q^80 + 23 * q^81 - 42 * q^82 - 48 * q^83 - 32 * q^84 - 27 * q^85 - 44 * q^86 - 12 * q^87 - 12 * q^88 - 45 * q^89 - 78 * q^90 - 64 * q^91 + 12 * q^92 - 20 * q^93 + 24 * q^94 + 24 * q^95 - 4 * q^96 + 46 * q^97 + 87 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)

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
74.2.a	\(\chi_{74}(1, \cdot)\)	74.2.a.a	2	1
		74.2.a.b	2
74.2.b	\(\chi_{74}(73, \cdot)\)	74.2.b.a	4	1
74.2.c	\(\chi_{74}(47, \cdot)\)	74.2.c.a	2	2
		74.2.c.b	2
		74.2.c.c	6
74.2.e	\(\chi_{74}(11, \cdot)\)	74.2.e.a	4	2
		74.2.e.b	4
74.2.f	\(\chi_{74}(7, \cdot)\)	74.2.f.a	6	6
		74.2.f.b	12
74.2.h	\(\chi_{74}(3, \cdot)\)	74.2.h.a	12	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)