Space of modular forms of level 13 and weight 10

• Label: 13.10
• Level: 13
• Weight: 10
• Dimension: 57
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 140
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 13 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(140\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(13))\).

	Total	New	Old
Modular forms	69	67	2
Cusp forms	57	57	0
Eisenstein series	12	10	2

Trace form

57 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 6 * q^5 - 6 * q^6 - 2058 * q^7 - 36870 * q^8 - 6 * q^9 + 153354 * q^10 - 18426 * q^11 - 414732 * q^12 - 108438 * q^13 + 363828 * q^14 + 596802 * q^15 - 6 * q^16 - 1407705 * q^17 + 996060 * q^18 - 945954 * q^19 + 47490 * q^20 + 1091994 * q^21 + 7251264 * q^22 + 1079118 * q^23 - 9699510 * q^24 - 5859387 * q^25 - 8735256 * q^26 + 3339312 * q^27 + 14239284 * q^28 + 24371211 * q^29 + 5598570 * q^30 - 21628782 * q^31 - 52435044 * q^32 - 17053806 * q^33 + 38183442 * q^34 + 62746314 * q^35 + 34768494 * q^36 - 53509041 * q^37 - 75064908 * q^38 - 80178942 * q^39 + 106596636 * q^40 + 56747037 * q^41 - 14526420 * q^42 - 80175066 * q^43 + 56834772 * q^44 + 73439469 * q^45 + 170228838 * q^46 - 6163842 * q^47 - 56937270 * q^48 - 34849122 * q^49 - 128608704 * q^50 - 71585676 * q^51 - 288763668 * q^52 - 114189792 * q^53 - 246491784 * q^54 + 163894998 * q^55 + 411453492 * q^56 + 565707582 * q^57 + 537801978 * q^58 + 154378806 * q^59 - 60832368 * q^60 - 782273979 * q^61 - 1008838710 * q^62 + 100702062 * q^63 + 550962348 * q^64 + 106769433 * q^65 - 1355116728 * q^66 - 1242683958 * q^67 - 336262764 * q^68 + 1099685022 * q^69 + 2304349956 * q^70 + 1546925586 * q^71 + 2551405308 * q^72 + 129804042 * q^73 - 504794946 * q^74 - 1302985644 * q^75 - 2241261522 * q^76 - 2326903116 * q^77 - 3971344908 * q^78 - 833767980 * q^79 + 3055272 * q^80 + 714226488 * q^81 + 2614660038 * q^82 + 3843007890 * q^83 + 6813050412 * q^84 + 1267441977 * q^85 + 2993016648 * q^86 + 2516626782 * q^87 - 5351686524 * q^88 - 5347573806 * q^89 - 16198597968 * q^90 - 6798799098 * q^91 - 2717293548 * q^92 + 2392035078 * q^93 + 8666109342 * q^94 + 7621807350 * q^95 + 10009032444 * q^96 + 4709667126 * q^97 + 8696899974 * q^98 + 7410530166 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.10.a	\(\chi_{13}(1, \cdot)\)	13.10.a.a	4	1
		13.10.a.b	5
13.10.b	\(\chi_{13}(12, \cdot)\)	13.10.b.a	10	1
13.10.c	\(\chi_{13}(3, \cdot)\)	13.10.c.a	18	2
13.10.e	\(\chi_{13}(4, \cdot)\)	13.10.e.a	20	2