Space of modular forms of level 3 and weight 8

• Label: 3.8
• Level: 3
• Weight: 8
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 5
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 3 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(3))\).

	Total	New	Old
Modular forms	3	1	2
Cusp forms	1	1	0
Eisenstein series	2	0	2

Trace form

q + 6 * q^2 - 27 * q^3 - 92 * q^4 + 390 * q^5 - 162 * q^6 - 64 * q^7 - 1320 * q^8 + 729 * q^9 + 2340 * q^10 - 948 * q^11 + 2484 * q^12 - 5098 * q^13 - 384 * q^14 - 10530 * q^15 + 3856 * q^16 + 28386 * q^17 + 4374 * q^18 - 8620 * q^19 - 35880 * q^20 + 1728 * q^21 - 5688 * q^22 - 15288 * q^23 + 35640 * q^24 + 73975 * q^25 - 30588 * q^26 - 19683 * q^27 + 5888 * q^28 + 36510 * q^29 - 63180 * q^30 - 276808 * q^31 + 192096 * q^32 + 25596 * q^33 + 170316 * q^34 - 24960 * q^35 - 67068 * q^36 + 268526 * q^37 - 51720 * q^38 + 137646 * q^39 - 514800 * q^40 - 629718 * q^41 + 10368 * q^42 + 685772 * q^43 + 87216 * q^44 + 284310 * q^45 - 91728 * q^46 + 583296 * q^47 - 104112 * q^48 - 819447 * q^49 + 443850 * q^50 - 766422 * q^51 + 469016 * q^52 - 428058 * q^53 - 118098 * q^54 - 369720 * q^55 + 84480 * q^56 + 232740 * q^57 + 219060 * q^58 + 1306380 * q^59 + 968760 * q^60 + 300662 * q^61 - 1660848 * q^62 - 46656 * q^63 + 659008 * q^64 - 1988220 * q^65 + 153576 * q^66 - 507244 * q^67 - 2611512 * q^68 + 412776 * q^69 - 149760 * q^70 + 5560632 * q^71 - 962280 * q^72 + 1369082 * q^73 + 1611156 * q^74 - 1997325 * q^75 + 793040 * q^76 + 60672 * q^77 + 825876 * q^78 - 6913720 * q^79 + 1503840 * q^80 + 531441 * q^81 - 3778308 * q^82 - 4376748 * q^83 - 158976 * q^84 + 11070540 * q^85 + 4114632 * q^86 - 985770 * q^87 + 1251360 * q^88 - 8528310 * q^89 + 1705860 * q^90 + 326272 * q^91 + 1406496 * q^92 + 7473816 * q^93 + 3499776 * q^94 - 3361800 * q^95 - 5186592 * q^96 - 8826814 * q^97 - 4916682 * q^98 - 691092 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.8.a	\(\chi_{3}(1, \cdot)\)	3.8.a.a	1	1