Space of modular forms of level 102 and weight 2

• Label: 102.2
• Level: 102
• Weight: 2
• Dimension: 73
• Nonzero newspaces: 5
• Newform subspaces: 9
• Sturm bound: 1152
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(102))\).

	Total	New	Old
Modular forms	352	73	279
Cusp forms	225	73	152
Eisenstein series	127	0	127

Trace form

73 * q + q^2 + q^3 + q^4 + 6 * q^5 + q^6 + 8 * q^7 + q^8 + q^9 - 2 * q^10 - 20 * q^11 - 7 * q^12 - 18 * q^13 - 24 * q^14 - 42 * q^15 - 7 * q^16 - 15 * q^17 - 31 * q^18 - 12 * q^19 - 2 * q^20 - 40 * q^21 - 20 * q^22 - 8 * q^23 - 7 * q^24 - 41 * q^25 + 6 * q^26 + q^27 + 8 * q^28 - 10 * q^29 + 6 * q^30 - 32 * q^31 + q^32 - 20 * q^33 + 17 * q^34 - 16 * q^35 + q^36 - 26 * q^37 + 20 * q^38 + 14 * q^39 + 6 * q^40 + 2 * q^41 + 56 * q^42 - 4 * q^43 + 12 * q^44 + 62 * q^45 + 24 * q^46 + 48 * q^47 + q^48 + 57 * q^49 + 31 * q^50 + 81 * q^51 + 14 * q^52 + 46 * q^53 + 57 * q^54 + 40 * q^55 + 8 * q^56 + 92 * q^57 + 30 * q^58 + 28 * q^59 + 38 * q^60 + 30 * q^61 + 32 * q^62 + 8 * q^63 + q^64 + 76 * q^65 + 20 * q^66 + 36 * q^67 + 9 * q^68 - 40 * q^69 - 16 * q^70 - 24 * q^71 - 7 * q^72 - 94 * q^73 - 34 * q^74 - 81 * q^75 + 20 * q^76 - 64 * q^77 - 50 * q^78 - 80 * q^79 - 26 * q^80 - 7 * q^81 - 94 * q^82 - 44 * q^83 - 24 * q^84 - 98 * q^85 - 20 * q^86 - 18 * q^87 - 52 * q^88 - 6 * q^89 - 2 * q^90 - 80 * q^91 - 8 * q^92 + 32 * q^93 - 80 * q^94 - 8 * q^95 + q^96 - 30 * q^97 - 15 * q^98 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)

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
102.2.a	\(\chi_{102}(1, \cdot)\)	102.2.a.a	1	1
		102.2.a.b	1
		102.2.a.c	1
102.2.b	\(\chi_{102}(67, \cdot)\)	102.2.b.a	2	1
102.2.f	\(\chi_{102}(13, \cdot)\)	102.2.f.a	4	2
102.2.h	\(\chi_{102}(19, \cdot)\)	102.2.h.a	8	4
		102.2.h.b	8
102.2.i	\(\chi_{102}(5, \cdot)\)	102.2.i.a	24	8
		102.2.i.b	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(102)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)