Space of modular forms of level 7 and weight 8

• Label: 7.8
• Level: 7
• Weight: 8
• Dimension: 11
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 32
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	17	15	2
Cusp forms	11	11	0
Eisenstein series	6	4	2

Trace form

11 * q - 3 * q^2 + 24 * q^3 - 259 * q^4 - 6 * q^5 + 1290 * q^6 + 329 * q^7 - 1833 * q^8 - 657 * q^9 - 9090 * q^10 + 1248 * q^11 + 20370 * q^12 - 4970 * q^13 + 46473 * q^14 - 5424 * q^15 - 89071 * q^16 - 71838 * q^17 - 45525 * q^18 + 46432 * q^19 + 375312 * q^20 + 141876 * q^21 - 226596 * q^22 - 229596 * q^23 - 472182 * q^24 - 61603 * q^25 + 294924 * q^26 + 528096 * q^27 + 587909 * q^28 + 130362 * q^29 - 1008786 * q^30 - 642716 * q^31 + 397719 * q^32 + 243132 * q^33 + 110238 * q^34 - 101598 * q^35 - 276783 * q^36 + 236422 * q^37 - 42144 * q^38 - 792288 * q^39 + 280008 * q^40 + 1045254 * q^41 + 190638 * q^42 - 559460 * q^43 + 2084964 * q^44 + 2350998 * q^45 - 842466 * q^46 - 3078228 * q^47 - 5738178 * q^48 - 2440837 * q^49 + 1878045 * q^50 + 2522532 * q^51 + 4828684 * q^52 + 3442014 * q^53 + 1151898 * q^54 - 5691408 * q^55 - 5335953 * q^56 + 5192496 * q^57 + 5748450 * q^58 + 1387200 * q^59 + 776580 * q^60 - 5179166 * q^61 - 7431576 * q^62 - 7166187 * q^63 - 2494543 * q^64 + 1905036 * q^65 + 5688126 * q^66 + 2371672 * q^67 - 881118 * q^68 + 13396392 * q^69 + 13492122 * q^70 + 759816 * q^71 - 3483969 * q^72 - 4226366 * q^73 - 15105120 * q^74 - 4136340 * q^75 + 2608018 * q^76 - 8195880 * q^77 - 16075920 * q^78 - 12023924 * q^79 - 16216512 * q^80 + 11466495 * q^81 + 29779974 * q^82 + 31439940 * q^83 + 35605458 * q^84 + 16342740 * q^85 - 19050576 * q^86 - 26728080 * q^87 - 2647104 * q^88 - 834462 * q^89 - 12292836 * q^90 - 5051018 * q^91 - 31021080 * q^92 - 35113668 * q^93 - 16931814 * q^94 + 320172 * q^95 + 34491954 * q^96 + 23705710 * q^97 + 59196165 * q^98 + 25873884 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.8.a	\(\chi_{7}(1, \cdot)\)	7.8.a.a	1	1
		7.8.a.b	2
7.8.c	\(\chi_{7}(2, \cdot)\)	7.8.c.a	8	2