Space of modular forms of level 13 and weight 6

• Label: 13.6
• Level: 13
• Weight: 6
• Dimension: 29
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 84
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(13))\).

	Total	New	Old
Modular forms	41	39	2
Cusp forms	29	29	0
Eisenstein series	12	10	2

Trace form

29 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 6 * q^5 - 6 * q^6 - 304 * q^7 + 570 * q^8 + 642 * q^9 + 54 * q^10 - 540 * q^11 - 2892 * q^12 - 1578 * q^13 - 540 * q^14 + 1182 * q^15 + 5114 * q^16 - 1203 * q^17 + 3432 * q^18 + 4982 * q^19 + 5490 * q^20 + 3660 * q^21 + 864 * q^22 - 3234 * q^23 - 24438 * q^24 - 9387 * q^25 - 17976 * q^26 - 15168 * q^27 - 22540 * q^28 + 159 * q^29 + 53130 * q^30 + 29816 * q^31 + 79260 * q^32 + 41316 * q^33 + 18354 * q^34 - 19536 * q^35 - 95346 * q^36 - 35995 * q^37 - 51996 * q^38 - 76998 * q^39 - 95844 * q^40 - 2727 * q^41 + 66108 * q^42 + 84460 * q^43 + 136884 * q^44 + 134919 * q^45 + 105414 * q^46 + 42696 * q^47 + 17034 * q^48 - 70052 * q^49 - 200964 * q^50 - 252180 * q^51 - 242500 * q^52 - 57348 * q^53 + 34920 * q^54 + 37248 * q^55 + 144276 * q^56 + 152748 * q^57 + 175830 * q^58 + 95760 * q^59 + 176112 * q^60 + 180189 * q^61 - 218694 * q^62 - 206640 * q^63 - 199380 * q^64 - 77307 * q^65 - 124536 * q^66 - 80158 * q^67 + 343716 * q^68 + 149208 * q^69 + 245556 * q^70 + 99822 * q^71 + 248604 * q^72 - 45730 * q^73 - 287574 * q^74 - 155904 * q^75 - 89746 * q^76 - 120840 * q^77 - 452892 * q^78 + 17160 * q^79 - 348408 * q^80 - 209730 * q^81 + 68418 * q^82 + 99132 * q^83 + 135660 * q^84 - 79383 * q^85 + 64296 * q^86 - 7758 * q^87 + 236484 * q^88 + 384570 * q^89 + 913152 * q^90 + 449384 * q^91 + 197076 * q^92 + 404976 * q^93 - 308370 * q^94 - 273330 * q^95 - 577764 * q^96 - 197518 * q^97 - 597306 * q^98 - 367068 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.6.a	\(\chi_{13}(1, \cdot)\)	13.6.a.a	2	1
		13.6.a.b	3
13.6.b	\(\chi_{13}(12, \cdot)\)	13.6.b.a	6	1
13.6.c	\(\chi_{13}(3, \cdot)\)	13.6.c.a	8	2
13.6.e	\(\chi_{13}(4, \cdot)\)	13.6.e.a	10	2