Space of modular forms of level 14 and weight 14

• Label: 14.14
• Level: 14
• Weight: 14
• Dimension: 22
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 168
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	84	22	62
Cusp forms	72	22	50
Eisenstein series	12	0	12

Trace form

22 * q + 2658 * q^3 - 8192 * q^4 + 12846 * q^5 - 113280 * q^6 - 382088 * q^7 - 3438246 * q^9 + 1155456 * q^10 - 13934604 * q^11 + 10887168 * q^12 + 33708770 * q^13 + 35452032 * q^14 - 151109688 * q^15 - 33554432 * q^16 - 45572208 * q^17 - 183558912 * q^18 - 282822898 * q^19 + 821944320 * q^20 - 513157806 * q^21 - 1416976128 * q^22 + 2808150888 * q^23 - 750256128 * q^24 - 996371738 * q^25 - 1887563136 * q^26 - 10681505172 * q^27 + 1788903424 * q^28 + 11758821408 * q^29 + 2408656128 * q^30 - 9271633756 * q^31 + 4313374584 * q^33 + 17188135680 * q^34 + 36911769762 * q^35 + 27498455040 * q^36 - 29593228264 * q^37 - 34253357184 * q^38 - 71382226392 * q^39 + 4732747776 * q^40 + 263744467848 * q^41 + 30614295936 * q^42 - 278396849068 * q^43 - 57076137984 * q^44 - 162333777138 * q^45 + 17435425536 * q^46 + 288153063036 * q^47 + 44593840128 * q^48 + 173173682710 * q^49 - 231469665024 * q^50 - 495671494140 * q^51 - 201358336000 * q^52 - 18582101220 * q^53 + 747862728192 * q^54 + 1194171358392 * q^55 - 21150302208 * q^56 - 1540320102948 * q^57 - 715506486528 * q^58 - 1773080057082 * q^59 + 768137232384 * q^60 + 1471912187606 * q^61 + 393014025984 * q^62 + 3622004475180 * q^63 + 1511828488192 * q^64 - 5013396201492 * q^65 - 4550836752384 * q^66 - 1885715579056 * q^67 - 186663763968 * q^68 + 11222669299536 * q^69 + 3403106646912 * q^70 - 305143351848 * q^71 - 751857303552 * q^72 - 7853502854308 * q^73 - 3784216506624 * q^74 + 2598390629190 * q^75 + 6694973038592 * q^76 + 11432830921428 * q^77 - 5309188091904 * q^78 - 11736575665336 * q^79 + 215520116736 * q^80 - 2933505361806 * q^81 + 440078045952 * q^82 + 887075655150 * q^83 - 1208568668160 * q^84 - 2124437327028 * q^85 - 302497813248 * q^86 - 9755550406692 * q^87 + 265845473280 * q^88 + 12796077806484 * q^89 + 8598252978048 * q^90 + 3187518646046 * q^91 + 8745915285504 * q^92 - 42999902503680 * q^93 - 14473100262912 * q^94 + 36159401606376 * q^95 - 3073049100288 * q^96 - 425201807104 * q^97 - 2608265565696 * q^98 - 11854055341428 * q^99

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

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
14.14.a	\(\chi_{14}(1, \cdot)\)	14.14.a.a	1	1
		14.14.a.b	1
		14.14.a.c	2
		14.14.a.d	2
14.14.c	\(\chi_{14}(9, \cdot)\)	14.14.c.a	8	2
		14.14.c.b	8

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

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