Space of modular forms of level 5 and weight 8

• Label: 5.8
• Level: 5
• Weight: 8
• Dimension: 5
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 16
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(5))\).

	Total	New	Old
Modular forms	9	7	2
Cusp forms	5	5	0
Eisenstein series	4	2	2

Trace form

5 * q + 6 * q^2 - 28 * q^3 + 188 * q^4 + 25 * q^5 - 1040 * q^6 - 1744 * q^7 + 2280 * q^8 + 7957 * q^9 + 1550 * q^10 - 8940 * q^11 - 26624 * q^12 + 7402 * q^13 + 39576 * q^14 + 8900 * q^15 - 29520 * q^16 - 39594 * q^17 + 29582 * q^18 + 26540 * q^19 - 1700 * q^20 + 36960 * q^21 + 103832 * q^22 - 111168 * q^23 - 269280 * q^24 - 86875 * q^25 + 107460 * q^26 + 305720 * q^27 + 53648 * q^28 - 102690 * q^29 + 158800 * q^30 + 314160 * q^31 + 100896 * q^32 - 449216 * q^33 - 619604 * q^34 - 419200 * q^35 - 184420 * q^36 - 12894 * q^37 + 702120 * q^38 + 1244984 * q^39 + 737000 * q^40 - 333990 * q^41 - 1649808 * q^42 - 75908 * q^43 + 1281936 * q^44 - 508175 * q^45 - 2114440 * q^46 - 502344 * q^47 + 1964032 * q^48 + 2007993 * q^49 + 963750 * q^50 + 741160 * q^51 - 1415784 * q^52 - 3672078 * q^53 - 2605760 * q^54 - 1570700 * q^55 + 835200 * q^56 + 2021840 * q^57 + 3386980 * q^58 + 420420 * q^59 + 2720800 * q^60 + 4095110 * q^61 + 4839072 * q^62 - 1831968 * q^63 - 9543232 * q^64 - 5423350 * q^65 - 1696480 * q^66 + 3719156 * q^67 - 5744952 * q^68 - 3256176 * q^69 + 2616600 * q^70 + 4761960 * q^71 + 1178760 * q^72 + 301582 * q^73 + 5924436 * q^74 + 2172500 * q^75 - 711600 * q^76 + 2894832 * q^77 + 7266064 * q^78 + 2212560 * q^79 - 7307600 * q^80 - 9376595 * q^81 - 12540308 * q^82 - 3652188 * q^83 + 5293536 * q^84 + 10330550 * q^85 + 2516160 * q^86 - 20541640 * q^87 + 10712160 * q^88 + 19324530 * q^89 + 2522150 * q^90 - 20224640 * q^91 - 6316944 * q^92 + 14003664 * q^93 + 11291656 * q^94 - 7058500 * q^95 + 2476160 * q^96 - 272394 * q^97 - 38814042 * q^98 - 12697996 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.8.a	\(\chi_{5}(1, \cdot)\)	5.8.a.a	1	1
		5.8.a.b	2
5.8.b	\(\chi_{5}(4, \cdot)\)	5.8.b.a	2	1