Space of modular forms of level 76 and weight 2

• Label: 76.2
• Level: 76
• Weight: 2
• Dimension: 87
• Nonzero newspaces: 6
• Newform subspaces: 6
• Sturm bound: 720
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(76))\).

	Total	New	Old
Modular forms	225	123	102
Cusp forms	136	87	49
Eisenstein series	89	36	53

Trace form

87 * q - 9 * q^2 - 9 * q^4 - 18 * q^5 - 9 * q^6 - 9 * q^8 - 18 * q^9 - 9 * q^10 - 9 * q^12 - 30 * q^13 - 9 * q^14 - 18 * q^15 - 9 * q^16 - 27 * q^17 - 21 * q^19 - 18 * q^20 - 39 * q^21 - 9 * q^22 - 9 * q^23 - 9 * q^24 - 36 * q^25 - 9 * q^26 - 3 * q^27 + 18 * q^28 + 54 * q^30 + 18 * q^31 + 36 * q^32 + 36 * q^33 + 36 * q^34 + 36 * q^35 + 81 * q^36 + 18 * q^37 + 54 * q^38 + 54 * q^39 + 54 * q^40 + 81 * q^42 + 33 * q^43 + 36 * q^44 + 9 * q^45 + 36 * q^46 - 9 * q^47 + 54 * q^48 - 21 * q^49 + 18 * q^50 - 36 * q^51 - 9 * q^52 - 54 * q^53 - 36 * q^54 - 36 * q^55 - 63 * q^57 - 18 * q^58 - 45 * q^59 - 12 * q^61 - 54 * q^62 - 12 * q^63 - 81 * q^64 - 9 * q^65 - 81 * q^66 + 15 * q^67 - 72 * q^68 + 99 * q^69 - 117 * q^70 - 9 * q^71 - 144 * q^72 + 60 * q^73 - 63 * q^74 + 42 * q^75 - 99 * q^76 + 81 * q^77 - 81 * q^78 + 24 * q^79 - 81 * q^80 + 27 * q^81 - 144 * q^82 - 9 * q^83 - 117 * q^84 + 90 * q^85 - 72 * q^86 - 36 * q^87 - 81 * q^88 + 9 * q^89 - 36 * q^90 - 12 * q^91 - 54 * q^92 - 48 * q^93 + 9 * q^95 + 54 * q^96 - 9 * q^97 + 90 * q^98 - 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)

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
76.2.a	\(\chi_{76}(1, \cdot)\)	76.2.a.a	1	1
76.2.d	\(\chi_{76}(75, \cdot)\)	76.2.d.a	8	1
76.2.e	\(\chi_{76}(45, \cdot)\)	76.2.e.a	2	2
76.2.f	\(\chi_{76}(27, \cdot)\)	76.2.f.a	16	2
76.2.i	\(\chi_{76}(5, \cdot)\)	76.2.i.a	12	6
76.2.k	\(\chi_{76}(3, \cdot)\)	76.2.k.a	48	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(76))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(76)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)