Space of modular forms of level 17 and weight 4

• Label: 17.4
• Level: 17
• Weight: 4
• Dimension: 28
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 96
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(17))\).

	Total	New	Old
Modular forms	44	42	2
Cusp forms	28	28	0
Eisenstein series	16	14	2

Trace form

28 * 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 - 112 * q^10 - 120 * q^11 - 104 * q^12 + 24 * q^13 + 152 * q^14 + 328 * q^15 + 432 * q^16 + 120 * q^17 + 432 * q^18 + 72 * q^19 + 104 * q^20 - 104 * q^21 - 232 * q^22 - 216 * q^23 - 1880 * q^24 - 1236 * q^25 - 1040 * q^26 - 224 * q^27 + 136 * q^28 + 252 * q^29 + 1336 * q^30 + 856 * q^31 + 1168 * q^32 + 1040 * q^33 + 2104 * q^34 + 976 * q^35 + 1656 * q^36 + 664 * q^37 - 336 * q^38 - 1224 * q^39 - 2504 * q^40 - 1428 * q^41 - 2936 * q^42 - 1472 * q^43 - 1960 * q^44 - 1348 * q^45 - 1016 * q^46 + 1512 * q^47 + 3296 * q^48 + 1528 * q^49 + 2784 * q^50 + 1592 * q^51 + 3056 * q^52 - 316 * q^53 - 2696 * q^54 - 1896 * q^55 - 1008 * q^56 - 2096 * q^57 - 1488 * q^58 - 872 * q^59 - 1424 * q^60 + 232 * q^61 - 1872 * q^62 + 1960 * q^63 - 2104 * q^64 + 1092 * q^65 + 5168 * q^66 + 2128 * q^67 + 3632 * q^68 + 3728 * q^69 + 1264 * q^70 + 184 * q^71 + 48 * q^72 + 292 * q^73 + 256 * q^74 + 856 * q^75 + 480 * q^76 - 216 * q^77 - 1792 * q^78 - 360 * q^79 - 872 * q^80 - 2992 * q^81 - 424 * q^82 - 5504 * q^83 - 8352 * q^84 - 4316 * q^85 - 8512 * q^86 - 1496 * q^87 + 1720 * q^88 - 1112 * q^89 - 1056 * q^90 + 1432 * q^91 + 3464 * q^92 + 2232 * q^93 + 3928 * q^94 + 3880 * q^95 + 5984 * q^96 + 280 * q^97 + 8568 * q^98 - 2616 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.4.a	\(\chi_{17}(1, \cdot)\)	17.4.a.a	1	1
		17.4.a.b	3
17.4.b	\(\chi_{17}(16, \cdot)\)	17.4.b.a	4	1
17.4.c	\(\chi_{17}(4, \cdot)\)	17.4.c.a	8	2
17.4.d	\(\chi_{17}(2, \cdot)\)	17.4.d.a	12	4