Space of modular forms of level 6 and weight 14

• Label: 6.14
• Level: 6
• Weight: 14
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 28
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(6))\).

	Total	New	Old
Modular forms	15	1	14
Cusp forms	11	1	10
Eisenstein series	4	0	4

Trace form

q + 64 * q^2 - 729 * q^3 + 4096 * q^4 + 54654 * q^5 - 46656 * q^6 + 176336 * q^7 + 262144 * q^8 + 531441 * q^9 + 3497856 * q^10 + 6612420 * q^11 - 2985984 * q^12 - 24028978 * q^13 + 11285504 * q^14 - 39842766 * q^15 + 16777216 * q^16 - 154665054 * q^17 + 34012224 * q^18 + 190034876 * q^19 + 223862784 * q^20 - 128548944 * q^21 + 423194880 * q^22 - 352957800 * q^23 - 191102976 * q^24 + 1766356591 * q^25 - 1537854592 * q^26 - 387420489 * q^27 + 722272256 * q^28 - 2804086266 * q^29 - 2549937024 * q^30 + 2763661208 * q^31 + 1073741824 * q^32 - 4820454180 * q^33 - 9898563456 * q^34 + 9637467744 * q^35 + 2176782336 * q^36 + 20030257622 * q^37 + 12162232064 * q^38 + 17517124962 * q^39 + 14327218176 * q^40 - 39624547206 * q^41 - 8227132416 * q^42 - 81486174844 * q^43 + 27084472320 * q^44 + 29045376414 * q^45 - 22589299200 * q^46 - 34136017440 * q^47 - 12230590464 * q^48 - 65794625511 * q^49 + 113046821824 * q^50 + 112750824366 * q^51 - 98422693888 * q^52 - 21810829986 * q^53 - 24794911296 * q^54 + 361395202680 * q^55 + 46225424384 * q^56 - 138535424604 * q^57 - 179461521024 * q^58 + 229219661220 * q^59 - 163195969536 * q^60 + 9799736750 * q^61 + 176874317312 * q^62 + 93712180176 * q^63 + 68719476736 * q^64 - 1313279763612 * q^65 - 308509067520 * q^66 + 789042707996 * q^67 - 633508061184 * q^68 + 257306236200 * q^69 + 616797935616 * q^70 - 369504705240 * q^71 + 139314069504 * q^72 - 693077725078 * q^73 + 1281936487808 * q^74 - 1287673954839 * q^75 + 778382852096 * q^76 + 1166007693120 * q^77 + 1121095997568 * q^78 + 2231309995208 * q^79 + 916941963264 * q^80 + 282429536481 * q^81 - 2535971021184 * q^82 + 2084328707772 * q^83 - 526536474624 * q^84 - 8453063861316 * q^85 - 5215115190016 * q^86 + 2044178887914 * q^87 + 1733406228480 * q^88 + 2221961096538 * q^89 + 1858904090496 * q^90 - 4237173864608 * q^91 - 1445715148800 * q^92 - 2014709020632 * q^93 - 2184705116160 * q^94 + 10386166112904 * q^95 - 782757789696 * q^96 + 10268379896642 * q^97 - 4210856032704 * q^98 + 3514111097220 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.14.a	\(\chi_{6}(1, \cdot)\)	6.14.a.a	1	1

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)