Space of modular forms of level 208 and weight 4

• Label: 208.4
• Level: 208
• Weight: 4
• Dimension: 2192
• Nonzero newspaces: 14
• Newform subspaces: 45
• Sturm bound: 10752
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 14 \)
Newform subspaces:			\( 45 \)
Sturm bound:			\(10752\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(208))\).

	Total	New	Old
Modular forms	4200	2290	1910
Cusp forms	3864	2192	1672
Eisenstein series	336	98	238

Trace form

2192 * q - 20 * q^2 - 22 * q^3 - 40 * q^4 - 22 * q^5 + 40 * q^6 + 30 * q^7 + 64 * q^8 + 16 * q^9 + 112 * q^10 - 142 * q^11 - 224 * q^12 - 50 * q^13 - 424 * q^14 + 246 * q^15 - 584 * q^16 - 146 * q^17 - 372 * q^18 + 122 * q^19 + 368 * q^20 + 58 * q^21 + 1152 * q^22 - 130 * q^23 + 1672 * q^24 + 230 * q^25 + 240 * q^26 - 100 * q^27 - 584 * q^28 - 22 * q^29 - 2496 * q^30 - 1074 * q^31 - 1960 * q^32 - 398 * q^33 - 896 * q^34 - 1066 * q^35 + 1168 * q^36 + 314 * q^37 + 2440 * q^38 - 1366 * q^39 + 2624 * q^40 - 1026 * q^41 + 1336 * q^42 + 754 * q^43 - 1760 * q^44 + 78 * q^45 - 2288 * q^46 + 4042 * q^47 - 3560 * q^48 + 1452 * q^49 - 1476 * q^50 + 6260 * q^51 + 212 * q^52 + 3532 * q^53 + 2728 * q^54 + 2966 * q^55 + 952 * q^56 + 1354 * q^57 - 40 * q^58 - 4946 * q^59 + 360 * q^60 - 5290 * q^61 + 136 * q^62 - 9690 * q^63 - 1048 * q^64 - 2662 * q^65 + 808 * q^66 - 5794 * q^67 + 1736 * q^68 - 1638 * q^69 - 344 * q^70 + 1438 * q^71 - 2208 * q^72 - 314 * q^73 + 880 * q^74 + 7020 * q^75 + 2432 * q^76 + 2612 * q^77 + 748 * q^78 + 7484 * q^79 + 5272 * q^80 - 558 * q^81 + 1384 * q^82 + 5578 * q^83 + 4288 * q^84 + 5930 * q^85 + 11936 * q^86 + 4482 * q^87 + 13360 * q^88 + 8838 * q^89 + 20832 * q^90 - 278 * q^91 + 2864 * q^92 + 4418 * q^93 + 3976 * q^94 - 15854 * q^95 - 11464 * q^96 - 4946 * q^97 - 16420 * q^98 - 16934 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.4.a	\(\chi_{208}(1, \cdot)\)	208.4.a.a	1	1
		208.4.a.b	1
		208.4.a.c	1
		208.4.a.d	1
		208.4.a.e	1
		208.4.a.f	1
		208.4.a.g	1
		208.4.a.h	2
		208.4.a.i	2
		208.4.a.j	2
		208.4.a.k	2
		208.4.a.l	3
208.4.b	\(\chi_{208}(105, \cdot)\)	None	0	1
208.4.e	\(\chi_{208}(25, \cdot)\)	None	0	1
208.4.f	\(\chi_{208}(129, \cdot)\)	208.4.f.a	2	1
		208.4.f.b	2
		208.4.f.c	2
		208.4.f.d	4
		208.4.f.e	10
208.4.i	\(\chi_{208}(81, \cdot)\)	208.4.i.a	2	2
		208.4.i.b	2
		208.4.i.c	2
		208.4.i.d	4
		208.4.i.e	4
		208.4.i.f	6
		208.4.i.g	8
		208.4.i.h	12
208.4.k	\(\chi_{208}(31, \cdot)\)	208.4.k.a	2	2
		208.4.k.b	12
		208.4.k.c	28
208.4.l	\(\chi_{208}(83, \cdot)\)	208.4.l.a	164	2
208.4.n	\(\chi_{208}(53, \cdot)\)	208.4.n.a	144	2
208.4.p	\(\chi_{208}(77, \cdot)\)	208.4.p.a	164	2
208.4.s	\(\chi_{208}(99, \cdot)\)	208.4.s.a	164	2
208.4.u	\(\chi_{208}(135, \cdot)\)	None	0	2
208.4.w	\(\chi_{208}(17, \cdot)\)	208.4.w.a	2	2
		208.4.w.b	2
		208.4.w.c	8
		208.4.w.d	8
		208.4.w.e	20
208.4.z	\(\chi_{208}(9, \cdot)\)	None	0	2
208.4.ba	\(\chi_{208}(121, \cdot)\)	None	0	2
208.4.bc	\(\chi_{208}(7, \cdot)\)	None	0	4
208.4.bf	\(\chi_{208}(11, \cdot)\)	208.4.bf.a	328	4
208.4.bh	\(\chi_{208}(69, \cdot)\)	208.4.bh.a	328	4
208.4.bj	\(\chi_{208}(29, \cdot)\)	208.4.bj.a	328	4
208.4.bk	\(\chi_{208}(115, \cdot)\)	208.4.bk.a	328	4
208.4.bm	\(\chi_{208}(15, \cdot)\)	208.4.bm.a	4	4
		208.4.bm.b	24
		208.4.bm.c	28
		208.4.bm.d	28

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

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