Space of modular forms of level 208 and weight 2

• Label: 208.2
• Level: 208
• Weight: 2
• Dimension: 698
• Nonzero newspaces: 14
• Newform subspaces: 34
• Sturm bound: 5376
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 14 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(5376\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(208))\).

	Total	New	Old
Modular forms	1512	796	716
Cusp forms	1177	698	479
Eisenstein series	335	98	237

Trace form

698 * q - 20 * q^2 - 14 * q^3 - 24 * q^4 - 26 * q^5 - 32 * q^6 - 18 * q^7 - 32 * q^8 - 6 * q^9 - 24 * q^10 - 22 * q^11 - 16 * q^12 - 28 * q^13 - 40 * q^14 - 26 * q^15 - 8 * q^16 - 46 * q^17 - 28 * q^18 - 30 * q^19 - 32 * q^20 - 38 * q^21 - 24 * q^22 - 18 * q^23 - 24 * q^24 - 12 * q^25 - 28 * q^26 - 20 * q^27 - 40 * q^28 - 42 * q^29 - 16 * q^30 + 14 * q^31 - 40 * q^32 - 46 * q^33 - 32 * q^34 - 10 * q^35 - 16 * q^36 - 42 * q^37 - 30 * q^39 - 32 * q^40 - 30 * q^41 - 24 * q^42 - 86 * q^43 - 16 * q^44 - 94 * q^45 - 48 * q^46 - 86 * q^47 - 40 * q^48 - 114 * q^49 - 12 * q^50 - 92 * q^51 - 20 * q^52 - 88 * q^53 - 24 * q^54 - 90 * q^55 - 8 * q^56 - 54 * q^57 - 42 * q^59 - 24 * q^60 - 54 * q^61 - 56 * q^62 - 74 * q^63 - 24 * q^64 - 82 * q^65 - 56 * q^66 - 10 * q^67 - 24 * q^68 - 6 * q^69 - 40 * q^70 - 18 * q^71 - 32 * q^72 - 6 * q^73 - 24 * q^74 - 12 * q^75 - 48 * q^76 - 44 * q^77 - 20 * q^78 - 36 * q^79 - 40 * q^80 - 92 * q^81 - 24 * q^82 - 14 * q^83 + 160 * q^84 - 14 * q^85 + 72 * q^86 + 18 * q^87 + 80 * q^88 + 90 * q^89 + 296 * q^90 + 26 * q^91 + 144 * q^92 + 130 * q^93 + 200 * q^94 + 66 * q^95 + 440 * q^96 + 50 * q^97 + 204 * q^98 + 82 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.2.a	\(\chi_{208}(1, \cdot)\)	208.2.a.a	1	1
		208.2.a.b	1
		208.2.a.c	1
		208.2.a.d	1
		208.2.a.e	2
208.2.b	\(\chi_{208}(105, \cdot)\)	None	0	1
208.2.e	\(\chi_{208}(25, \cdot)\)	None	0	1
208.2.f	\(\chi_{208}(129, \cdot)\)	208.2.f.a	2	1
		208.2.f.b	4
208.2.i	\(\chi_{208}(81, \cdot)\)	208.2.i.a	2	2
		208.2.i.b	2
		208.2.i.c	2
		208.2.i.d	2
		208.2.i.e	4
208.2.k	\(\chi_{208}(31, \cdot)\)	208.2.k.a	2	2
		208.2.k.b	12
208.2.l	\(\chi_{208}(83, \cdot)\)	208.2.l.a	2	2
		208.2.l.b	50
208.2.n	\(\chi_{208}(53, \cdot)\)	208.2.n.a	48	2
208.2.p	\(\chi_{208}(77, \cdot)\)	208.2.p.a	8	2
		208.2.p.b	44
208.2.s	\(\chi_{208}(99, \cdot)\)	208.2.s.a	2	2
		208.2.s.b	50
208.2.u	\(\chi_{208}(135, \cdot)\)	None	0	2
208.2.w	\(\chi_{208}(17, \cdot)\)	208.2.w.a	2	2
		208.2.w.b	2
		208.2.w.c	8
208.2.z	\(\chi_{208}(9, \cdot)\)	None	0	2
208.2.ba	\(\chi_{208}(121, \cdot)\)	None	0	2
208.2.bc	\(\chi_{208}(7, \cdot)\)	None	0	4
208.2.bf	\(\chi_{208}(11, \cdot)\)	208.2.bf.a	104	4
208.2.bh	\(\chi_{208}(69, \cdot)\)	208.2.bh.a	104	4
208.2.bj	\(\chi_{208}(29, \cdot)\)	208.2.bj.a	104	4
208.2.bk	\(\chi_{208}(115, \cdot)\)	208.2.bk.a	104	4
208.2.bm	\(\chi_{208}(15, \cdot)\)	208.2.bm.a	4	4
		208.2.bm.b	4
		208.2.bm.c	4
		208.2.bm.d	4
		208.2.bm.e	4
		208.2.bm.f	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(208)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)