Space of modular forms of level 13 and weight 8

• Label: 13.8
• Level: 13
• Weight: 8
• Dimension: 43
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 112
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 13 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(13))\).

	Total	New	Old
Modular forms	55	53	2
Cusp forms	43	43	0
Eisenstein series	12	10	2

Trace form

43 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 6 * q^5 - 6 * q^6 - 1520 * q^7 + 4602 * q^8 - 5838 * q^9 - 9966 * q^10 + 3948 * q^11 + 34548 * q^12 + 14958 * q^13 - 10860 * q^14 - 41154 * q^15 - 81926 * q^16 - 65769 * q^17 + 249780 * q^18 + 153526 * q^19 - 106302 * q^20 - 342192 * q^21 - 219216 * q^22 + 14958 * q^23 + 502602 * q^24 + 234363 * q^25 + 409464 * q^26 + 154176 * q^27 - 681548 * q^28 + 76953 * q^29 - 626262 * q^30 - 258056 * q^31 - 1050948 * q^32 + 36528 * q^33 + 700050 * q^34 + 399624 * q^35 + 320958 * q^36 - 249245 * q^37 + 1975380 * q^38 - 369030 * q^39 + 2796252 * q^40 + 2173287 * q^41 + 619068 * q^42 - 1491724 * q^43 - 6740220 * q^44 - 7009371 * q^45 - 6362874 * q^46 - 520680 * q^47 + 4751178 * q^48 + 5470856 * q^49 + 7643448 * q^50 + 5202828 * q^51 + 6489628 * q^52 + 5697084 * q^53 + 5023944 * q^54 - 3327552 * q^55 - 12589788 * q^56 - 14632344 * q^57 - 15795486 * q^58 - 7107960 * q^59 - 10369728 * q^60 + 2597415 * q^61 + 213786 * q^62 + 24945120 * q^63 + 42145260 * q^64 + 25073715 * q^65 + 13473096 * q^66 - 10324958 * q^67 - 20309340 * q^68 - 20351532 * q^69 - 38565900 * q^70 - 19914258 * q^71 - 46047252 * q^72 - 12678410 * q^73 + 368070 * q^74 + 25169952 * q^75 + 59478862 * q^76 + 44006880 * q^77 + 85447572 * q^78 + 15844488 * q^79 + 9329784 * q^80 - 27657246 * q^81 - 52917618 * q^82 - 35849820 * q^83 - 80552724 * q^84 - 66082509 * q^85 - 61274616 * q^86 + 12139794 * q^87 + 50076132 * q^88 + 53885130 * q^89 + 128173584 * q^90 + 43758208 * q^91 + 88422900 * q^92 + 601932 * q^93 - 15292674 * q^94 - 80709522 * q^95 - 200332404 * q^96 - 74861486 * q^97 - 47531130 * q^98 - 2915364 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.8.a	\(\chi_{13}(1, \cdot)\)	13.8.a.a	1	1
		13.8.a.b	2
		13.8.a.c	4
13.8.b	\(\chi_{13}(12, \cdot)\)	13.8.b.a	6	1
13.8.c	\(\chi_{13}(3, \cdot)\)	13.8.c.a	16	2
13.8.e	\(\chi_{13}(4, \cdot)\)	13.8.e.a	14	2