Space of modular forms of level 14 and weight 16

• Label: 14.16
• Level: 14
• Weight: 16
• Dimension: 28
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 192
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	96	28	68
Cusp forms	84	28	56
Eisenstein series	12	0	12

Trace form

28 * q + 256 * q^2 - 3756 * q^3 - 32768 * q^4 + 285996 * q^5 - 79104 * q^6 + 6429592 * q^7 + 4194304 * q^8 - 47565984 * q^9 + 74524416 * q^10 + 33436410 * q^11 - 61538304 * q^12 - 755035930 * q^13 - 192649472 * q^14 + 1600194228 * q^15 - 536870912 * q^16 - 4080005850 * q^17 + 13212307200 * q^18 - 9141926860 * q^19 - 10645831680 * q^20 + 25282853328 * q^21 + 5988020736 * q^22 - 2758427574 * q^23 - 3913285632 * q^24 + 120714270220 * q^25 + 59389229312 * q^26 - 259366107312 * q^27 + 51658719232 * q^28 + 166923506772 * q^29 - 176941857792 * q^30 - 27407735590 * q^31 + 68719476736 * q^32 + 600762731118 * q^33 - 977368691712 * q^34 - 254178109500 * q^35 + 2310986072064 * q^36 + 149501070998 * q^37 + 680733350144 * q^38 - 5160046935828 * q^39 + 1221008031744 * q^40 + 774096412212 * q^41 + 2636743236864 * q^42 - 7608084350236 * q^43 + 547822141440 * q^44 + 8191933970142 * q^45 + 6517917729792 * q^46 - 22499484843930 * q^47 - 4530653626368 * q^48 - 1054043593700 * q^49 + 19770420630784 * q^50 + 4877277256998 * q^51 - 2461611163648 * q^52 + 16890448302834 * q^53 + 10438917788160 * q^54 - 82843153534188 * q^55 + 6975391793152 * q^56 - 888707475096 * q^57 + 37836850510848 * q^58 + 34826010431712 * q^59 - 19996244803584 * q^60 + 17764201919300 * q^61 + 49843200430592 * q^62 - 249097382788008 * q^63 + 123145302310912 * q^64 + 282008770328544 * q^65 + 102986333460480 * q^66 + 51589501420622 * q^67 - 66846815846400 * q^68 - 382281948276804 * q^69 - 195442965532416 * q^70 - 139102867007928 * q^71 + 216470441164800 * q^72 + 795700735942514 * q^73 - 50714292542464 * q^74 - 715692370365006 * q^75 - 272006879543296 * q^76 - 417658274857614 * q^77 + 37599291531264 * q^78 + 878030081386874 * q^79 + 76771466674176 * q^80 + 929178184777770 * q^81 - 842153458771968 * q^82 - 2321219092488174 * q^83 - 471920575315968 * q^84 + 1894789332089160 * q^85 + 566915957886464 * q^86 + 3615368443152696 * q^87 + 208807762329600 * q^88 - 1635224180138790 * q^89 - 4239571384073472 * q^90 - 3013237483489510 * q^91 + 1026855547502592 * q^92 + 5138898435555006 * q^93 + 2093972251614720 * q^94 - 832725641566938 * q^95 - 64115271794688 * q^96 - 5168668714908820 * q^97 - 2045051439820544 * q^98 + 1427989031154660 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.16.a	\(\chi_{14}(1, \cdot)\)	14.16.a.a	1	1
		14.16.a.b	2
		14.16.a.c	2
		14.16.a.d	3
14.16.c	\(\chi_{14}(9, \cdot)\)	14.16.c.a	10	2
		14.16.c.b	10

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)