Space of modular forms of level 17 and weight 10

• Label: 17.10
• Level: 17
• Weight: 10
• Dimension: 100
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 240
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 17 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(17))\).

	Total	New	Old
Modular forms	116	114	2
Cusp forms	100	100	0
Eisenstein series	16	14	2

Trace form

100 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 30792 * q^10 - 30136 * q^11 - 448520 * q^12 + 188888 * q^13 + 485112 * q^14 - 483512 * q^15 - 1835024 * q^16 - 308872 * q^17 + 1867248 * q^18 + 1110152 * q^19 + 2573304 * q^20 - 2576552 * q^21 - 4872456 * q^22 - 1546072 * q^23 + 15962728 * q^24 + 11840804 * q^25 - 26517800 * q^26 - 11494880 * q^27 + 9370504 * q^28 + 14629412 * q^29 + 43073848 * q^30 + 1635544 * q^31 - 29445424 * q^32 - 37949488 * q^33 - 61465544 * q^34 - 2054448 * q^35 + 71799480 * q^36 + 62997976 * q^37 + 11070208 * q^38 + 92266680 * q^39 - 59333192 * q^40 - 141781468 * q^41 - 349918040 * q^42 - 28756160 * q^43 + 300073048 * q^44 + 292612772 * q^45 + 7112008 * q^46 + 80549352 * q^47 - 113473312 * q^48 - 147967496 * q^49 - 350000016 * q^50 - 175275208 * q^51 - 148045840 * q^52 - 129469876 * q^53 + 1076768104 * q^54 + 603656600 * q^55 + 484286992 * q^56 - 593808704 * q^57 - 762251920 * q^58 - 478840296 * q^59 - 370566992 * q^60 + 432514312 * q^61 + 787144208 * q^62 + 1496567464 * q^63 + 1195591112 * q^64 - 286405668 * q^65 - 2553133984 * q^66 - 644835888 * q^67 - 2463221568 * q^68 - 383319472 * q^69 + 1338707696 * q^70 + 511118008 * q^71 + 1019013456 * q^72 + 328534492 * q^73 + 259703656 * q^74 + 1064858584 * q^75 + 617679776 * q^76 - 345339448 * q^77 - 2269165696 * q^78 - 475417960 * q^79 - 220853224 * q^80 + 500662400 * q^81 + 904295904 * q^82 - 319642368 * q^83 - 1547731872 * q^84 - 1519695380 * q^85 + 3356413696 * q^86 - 1212935960 * q^87 - 2282499656 * q^88 - 2724297272 * q^89 - 2735441976 * q^90 + 2147533336 * q^91 + 7534157896 * q^92 + 4908431928 * q^93 + 6950755288 * q^94 + 4494061800 * q^95 + 2578069856 * q^96 - 2922002216 * q^97 - 5864386752 * q^98 - 7407555576 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.10.a	\(\chi_{17}(1, \cdot)\)	17.10.a.a	5	1
		17.10.a.b	7
17.10.b	\(\chi_{17}(16, \cdot)\)	17.10.b.a	12	1
17.10.c	\(\chi_{17}(4, \cdot)\)	17.10.c.a	24	2
17.10.d	\(\chi_{17}(2, \cdot)\)	17.10.d.a	52	4