Space of modular forms of level 17 and weight 5

• Label: 17.5
• Level: 17
• Weight: 5
• Dimension: 40
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 120
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 17 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(17))\).

	Total	New	Old
Modular forms	56	56	0
Cusp forms	40	40	0
Eisenstein series	16	16	0

Trace form

40 * 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 + 376 * q^10 + 112 * q^11 - 776 * q^12 - 416 * q^13 - 776 * q^14 - 704 * q^15 + 256 * q^17 + 2032 * q^18 + 688 * q^19 + 2680 * q^20 + 2032 * q^21 + 760 * q^22 - 176 * q^23 + 1672 * q^24 - 2600 * q^26 - 2600 * q^27 - 7448 * q^28 - 3368 * q^29 - 9800 * q^30 - 3720 * q^31 - 2400 * q^32 + 4280 * q^34 + 4208 * q^35 + 11960 * q^36 + 7416 * q^37 + 16720 * q^38 + 15624 * q^39 + 20280 * q^40 + 2656 * q^41 - 6392 * q^42 - 7512 * q^43 - 31592 * q^44 - 23368 * q^45 - 25752 * q^46 - 10208 * q^47 - 14080 * q^48 - 3112 * q^49 + 3224 * q^51 + 12784 * q^52 + 24424 * q^53 + 51672 * q^54 + 26648 * q^55 + 40432 * q^56 + 10352 * q^57 - 4336 * q^58 - 3176 * q^59 - 38896 * q^60 - 24600 * q^61 - 39248 * q^62 - 55664 * q^63 - 45560 * q^64 - 37928 * q^65 - 29376 * q^66 + 34912 * q^68 + 46592 * q^69 + 59536 * q^70 + 21736 * q^71 + 59824 * q^72 + 28592 * q^73 + 15976 * q^74 + 46168 * q^75 - 9280 * q^76 + 2392 * q^77 - 6048 * q^78 - 15912 * q^79 - 47640 * q^80 - 48696 * q^81 - 58368 * q^82 - 27296 * q^83 + 18872 * q^85 + 74336 * q^86 + 38536 * q^87 + 55608 * q^88 - 1232 * q^89 - 24136 * q^90 - 7800 * q^91 - 27032 * q^92 - 32232 * q^93 - 37096 * q^94 - 49640 * q^95 - 79696 * q^96 - 12392 * q^97 - 76304 * q^98 + 6056 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(17))\)

We only show spaces with odd 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
17.5.e	\(\chi_{17}(3, \cdot)\)	17.5.e.a	40	8