Space of modular forms of level 208 and weight 10

• Label: 208.10
• Level: 208
• Weight: 10
• Dimension: 6674
• Nonzero newspaces: 14
• Sturm bound: 26880
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(26880\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(208))\).

	Total	New	Old
Modular forms	12264	6772	5492
Cusp forms	11928	6674	5254
Eisenstein series	336	98	238

Trace form

6674 * q - 20 * q^2 + 146 * q^3 - 360 * q^4 + 694 * q^5 + 4360 * q^6 - 2770 * q^7 + 1408 * q^8 - 11630 * q^9 - 9392 * q^10 - 109750 * q^11 - 434336 * q^12 + 43052 * q^13 + 267032 * q^14 - 930906 * q^15 + 1634488 * q^16 - 344254 * q^17 - 4359828 * q^18 + 1554434 * q^19 + 6555952 * q^20 + 594778 * q^21 + 68576 * q^22 - 2699346 * q^23 - 3727736 * q^24 + 60924 * q^25 + 6347744 * q^26 - 2718676 * q^27 - 7259080 * q^28 - 2181018 * q^29 + 9355584 * q^30 - 5338866 * q^31 + 3311960 * q^32 + 7058002 * q^33 + 9056384 * q^34 + 9687158 * q^35 - 47128304 * q^36 - 388058 * q^37 + 29992680 * q^38 - 103957438 * q^39 + 23502528 * q^40 + 13090002 * q^41 - 210798344 * q^42 + 34938378 * q^43 + 188446688 * q^44 + 147284754 * q^45 - 30864816 * q^46 - 310798934 * q^47 - 15663080 * q^48 + 169354118 * q^49 + 12579036 * q^50 - 27036316 * q^51 + 28284404 * q^52 + 45741560 * q^53 - 210622040 * q^54 + 96478438 * q^55 - 53022536 * q^56 + 422866378 * q^57 + 356543544 * q^58 + 149257206 * q^59 - 458068248 * q^60 - 880486982 * q^61 + 273577864 * q^62 - 440849418 * q^63 + 698585832 * q^64 + 864786782 * q^65 - 384547736 * q^66 - 1375020586 * q^67 + 571514952 * q^68 - 1007670150 * q^69 - 1212102424 * q^70 + 78348078 * q^71 - 1764151392 * q^72 + 31471530 * q^73 - 247821744 * q^74 + 1525237524 * q^75 + 906538176 * q^76 - 332087468 * q^77 + 1735024780 * q^78 - 3144507812 * q^79 + 1400545688 * q^80 + 1776840156 * q^81 + 1348575144 * q^82 + 1756794130 * q^83 - 1595353280 * q^84 + 3919284562 * q^85 - 7471037952 * q^86 - 1132827822 * q^87 - 9139514960 * q^88 + 1760912010 * q^89 + 18355821504 * q^90 + 438117850 * q^91 + 15151204272 * q^92 + 3089758082 * q^93 - 1958054392 * q^94 + 10263452418 * q^95 - 31072808392 * q^96 - 6907333598 * q^97 - 7482726564 * q^98 - 15380541518 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(208))\)

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
208.10.a	\(\chi_{208}(1, \cdot)\)	208.10.a.a	1	1
		208.10.a.b	1
		208.10.a.c	1
		208.10.a.d	3
		208.10.a.e	3
		208.10.a.f	4
		208.10.a.g	4
		208.10.a.h	5
		208.10.a.i	5
		208.10.a.j	6
		208.10.a.k	6
		208.10.a.l	7
		208.10.a.m	8
208.10.b	\(\chi_{208}(105, \cdot)\)	None	0	1
208.10.e	\(\chi_{208}(25, \cdot)\)	None	0	1
208.10.f	\(\chi_{208}(129, \cdot)\)	208.10.f.a	10	1
		208.10.f.b	10
		208.10.f.c	10
		208.10.f.d	32
208.10.i	\(\chi_{208}(81, \cdot)\)	n/a	124	2
208.10.k	\(\chi_{208}(31, \cdot)\)	n/a	126	2
208.10.l	\(\chi_{208}(83, \cdot)\)	n/a	500	2
208.10.n	\(\chi_{208}(53, \cdot)\)	n/a	432	2
208.10.p	\(\chi_{208}(77, \cdot)\)	n/a	500	2
208.10.s	\(\chi_{208}(99, \cdot)\)	n/a	500	2
208.10.u	\(\chi_{208}(135, \cdot)\)	None	0	2
208.10.w	\(\chi_{208}(17, \cdot)\)	n/a	124	2
208.10.z	\(\chi_{208}(9, \cdot)\)	None	0	2
208.10.ba	\(\chi_{208}(121, \cdot)\)	None	0	2
208.10.bc	\(\chi_{208}(7, \cdot)\)	None	0	4
208.10.bf	\(\chi_{208}(11, \cdot)\)	n/a	1000	4
208.10.bh	\(\chi_{208}(69, \cdot)\)	n/a	1000	4
208.10.bj	\(\chi_{208}(29, \cdot)\)	n/a	1000	4
208.10.bk	\(\chi_{208}(115, \cdot)\)	n/a	1000	4
208.10.bm	\(\chi_{208}(15, \cdot)\)	n/a	252	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(208))\) into lower level spaces

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