Properties

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

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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

\( 11 q + 62 q^{2} + 1196 q^{3} - 12292 q^{4} + 40195 q^{5} + 14512 q^{6} - 168008 q^{7} + 1846920 q^{8} - 6392573 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

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 the 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