Space of modular forms of level 5 and weight 14

• Label: 5.14
• Level: 5
• Weight: 14
• Dimension: 11
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 28
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 5 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(5))\).

	Total	New	Old
Modular forms	15	13	2
Cusp forms	11	11	0
Eisenstein series	4	2	2

Trace form

11 * q + 62 * q^2 + 1196 * q^3 - 12292 * q^4 + 40195 * q^5 + 14512 * q^6 - 168008 * q^7 + 1846920 * q^8 - 6392573 * q^9 + 11038470 * q^10 - 2853148 * q^11 - 7307408 * q^12 - 26984114 * q^13 + 60737976 * q^14 - 104603860 * q^15 + 141237296 * q^16 + 83763002 * q^17 - 157042234 * q^18 - 336593300 * q^19 - 8097940 * q^20 + 885170832 * q^21 + 829250184 * q^22 + 938237976 * q^23 - 7404019200 * q^24 - 156485725 * q^25 + 8251935572 * q^26 + 6840734120 * q^27 - 9175428416 * q^28 - 3163028150 * q^29 - 21689022560 * q^30 + 21602641312 * q^31 + 47124742432 * q^32 - 15740664128 * q^33 - 80063093604 * q^34 - 14617279080 * q^35 + 102917290076 * q^36 + 53280246022 * q^37 - 20522011720 * q^38 - 184848137176 * q^39 - 54972303000 * q^40 + 160108498342 * q^41 + 183672177984 * q^42 - 35580322844 * q^43 - 230870890544 * q^44 - 106921017485 * q^45 + 245905295832 * q^46 + 124790088032 * q^47 - 182851529024 * q^48 + 153256079943 * q^49 - 173205960850 * q^50 - 77091909128 * q^51 - 179398257128 * q^52 + 45099752246 * q^53 + 597835612000 * q^54 + 592862290740 * q^55 - 975459261600 * q^56 - 993398437360 * q^57 + 876855259620 * q^58 - 173431752700 * q^59 + 1360846735120 * q^60 - 1778406151598 * q^61 - 1356767292096 * q^62 + 1021221430056 * q^63 + 5479493674688 * q^64 - 603776760410 * q^65 - 4586012967616 * q^66 - 1916484488948 * q^67 - 702944699096 * q^68 + 4173254372544 * q^69 + 727995637320 * q^70 + 542334162232 * q^71 - 4905432210840 * q^72 + 1948560188626 * q^73 - 112699037564 * q^74 + 4254449522300 * q^75 - 2705620336400 * q^76 + 2438453692944 * q^77 - 1260878170928 * q^78 - 5453176298000 * q^79 - 2350867102480 * q^80 + 1245094354531 * q^81 + 5711708077164 * q^82 + 1238839864716 * q^83 - 9889103174304 * q^84 - 272111030430 * q^85 + 31279941882752 * q^86 + 7315958847560 * q^87 - 12297158950560 * q^88 - 29263478676450 * q^89 - 28129082707810 * q^90 + 6452491811792 * q^91 + 39896707925952 * q^92 - 1545330136368 * q^93 - 86477245944 * q^94 - 9217460052500 * q^95 + 32090410783232 * q^96 + 7656084054682 * q^97 - 27831437745266 * q^98 - 41874373276636 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.14.a	\(\chi_{5}(1, \cdot)\)	5.14.a.a	2	1
		5.14.a.b	3
5.14.b	\(\chi_{5}(4, \cdot)\)	5.14.b.a	6	1