Space of modular forms of level 104 and weight 2

• Label: 104.2
• Level: 104
• Weight: 2
• Dimension: 165
• Nonzero newspaces: 10
• Newform subspaces: 19
• Sturm bound: 1344
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1344\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(104))\).

	Total	New	Old
Modular forms	408	209	199
Cusp forms	265	165	100
Eisenstein series	143	44	99

Trace form

165 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 24 * q^9 - 12 * q^10 - 12 * q^11 - 12 * q^12 - 24 * q^14 - 12 * q^15 - 12 * q^16 - 27 * q^17 - 12 * q^18 - 24 * q^19 - 12 * q^20 - 24 * q^21 - 12 * q^22 - 24 * q^23 - 12 * q^24 - 39 * q^25 - 12 * q^26 - 60 * q^27 - 12 * q^28 - 15 * q^29 - 12 * q^30 - 24 * q^31 - 12 * q^32 - 48 * q^33 - 12 * q^34 - 24 * q^35 + 24 * q^36 - 3 * q^37 - 12 * q^38 + 24 * q^40 - 15 * q^41 + 60 * q^42 + 36 * q^43 + 48 * q^44 + 45 * q^45 + 108 * q^46 + 24 * q^47 + 84 * q^48 - 12 * q^49 + 96 * q^50 + 72 * q^51 + 96 * q^52 + 36 * q^53 + 96 * q^54 + 60 * q^55 + 96 * q^56 - 12 * q^57 + 84 * q^58 + 24 * q^59 + 108 * q^60 + 45 * q^61 + 48 * q^62 + 12 * q^63 + 60 * q^64 - 51 * q^65 + 24 * q^66 - 24 * q^67 - 12 * q^68 - 36 * q^69 + 48 * q^70 - 60 * q^71 - 12 * q^72 - 72 * q^73 - 12 * q^74 - 36 * q^75 - 12 * q^76 - 48 * q^77 - 12 * q^78 - 48 * q^79 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 72 * q^83 - 96 * q^84 - 39 * q^85 - 60 * q^86 + 12 * q^87 - 72 * q^88 - 24 * q^89 - 168 * q^90 + 60 * q^91 - 96 * q^92 + 36 * q^93 - 108 * q^94 + 84 * q^95 - 228 * q^96 + 12 * q^97 - 120 * q^98 + 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)

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
104.2.a	\(\chi_{104}(1, \cdot)\)	104.2.a.a	1	1
		104.2.a.b	2
104.2.b	\(\chi_{104}(53, \cdot)\)	104.2.b.a	2	1
		104.2.b.b	4
		104.2.b.c	6
104.2.e	\(\chi_{104}(77, \cdot)\)	104.2.e.a	2	1
		104.2.e.b	2
		104.2.e.c	8
104.2.f	\(\chi_{104}(25, \cdot)\)	104.2.f.a	4	1
104.2.i	\(\chi_{104}(9, \cdot)\)	104.2.i.a	2	2
		104.2.i.b	4
104.2.k	\(\chi_{104}(31, \cdot)\)	None	0	2
104.2.m	\(\chi_{104}(83, \cdot)\)	104.2.m.a	4	2
		104.2.m.b	20
104.2.o	\(\chi_{104}(17, \cdot)\)	104.2.o.a	8	2
104.2.r	\(\chi_{104}(29, \cdot)\)	104.2.r.a	24	2
104.2.s	\(\chi_{104}(69, \cdot)\)	104.2.s.a	4	2
		104.2.s.b	4
		104.2.s.c	16
104.2.u	\(\chi_{104}(11, \cdot)\)	104.2.u.a	48	4
104.2.w	\(\chi_{104}(7, \cdot)\)	None	0	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)