Space of modular forms of level 14 and weight 8

• Label: 14.8
• Level: 14
• Weight: 8
• Dimension: 12
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 96
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	48	12	36
Cusp forms	36	12	24
Eisenstein series	12	0	12

Trace form

12 * q + 16 * q^2 - 78 * q^3 + 426 * q^5 - 1104 * q^6 - 1680 * q^7 + 1024 * q^8 + 7656 * q^9 - 3984 * q^10 - 9228 * q^11 - 4992 * q^12 + 20346 * q^13 - 18704 * q^14 + 5208 * q^15 + 83256 * q^17 - 25872 * q^18 - 9642 * q^19 - 21120 * q^20 - 187110 * q^21 + 8736 * q^22 + 82848 * q^23 + 101376 * q^24 + 268080 * q^25 - 68464 * q^26 - 482292 * q^27 - 53760 * q^28 + 99468 * q^29 + 489408 * q^30 + 204324 * q^31 + 65536 * q^32 - 1098084 * q^33 - 236352 * q^34 + 156450 * q^35 + 694272 * q^36 + 182568 * q^37 - 699376 * q^38 + 820224 * q^39 - 254976 * q^40 - 458100 * q^41 + 1169616 * q^42 + 2293212 * q^43 - 590592 * q^44 - 2983938 * q^45 - 118080 * q^46 + 1549020 * q^47 - 319488 * q^48 + 837900 * q^49 - 4155056 * q^50 - 6552756 * q^51 - 1009536 * q^52 + 1444596 * q^53 + 4365216 * q^54 + 15553512 * q^55 + 1383424 * q^56 + 898332 * q^57 - 1177152 * q^58 - 10008282 * q^59 - 4137984 * q^60 - 2006454 * q^61 - 3245536 * q^62 - 4245276 * q^63 + 3145728 * q^64 - 4943316 * q^65 + 2043264 * q^66 + 5548776 * q^67 + 5328384 * q^68 + 6655752 * q^69 + 12656784 * q^70 + 7056504 * q^71 - 1655808 * q^72 - 957276 * q^73 - 4063936 * q^74 - 24940746 * q^75 - 8960640 * q^76 - 16124304 * q^77 - 10532352 * q^78 + 23562912 * q^79 + 1744896 * q^80 + 6576996 * q^81 + 19891584 * q^82 - 22146930 * q^83 + 13195392 * q^84 + 12208980 * q^85 + 14237408 * q^86 + 30809124 * q^87 - 4724736 * q^88 - 20862564 * q^89 - 61136592 * q^90 - 36790026 * q^91 - 16009728 * q^92 + 2129100 * q^93 + 29230944 * q^94 + 42512352 * q^95 + 6488064 * q^96 + 25969044 * q^97 + 26719504 * q^98 + 32055492 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.8.a	\(\chi_{14}(1, \cdot)\)	14.8.a.a	1	1
		14.8.a.b	1
		14.8.a.c	2
14.8.c	\(\chi_{14}(9, \cdot)\)	14.8.c.a	4	2
		14.8.c.b	4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 1}\)