Properties

Label 8.14
Level 8
Weight 14
Dimension 15
Nonzero newspaces 2
Newforms 4
Sturm bound 56
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 29 17 12
Cusp forms 23 15 8
Eisenstein series 6 2 4

Trace form

\(15q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 860q^{3} \) \(\mathstrut -\mathstrut 8556q^{4} \) \(\mathstrut +\mathstrut 14146q^{5} \) \(\mathstrut +\mathstrut 58444q^{6} \) \(\mathstrut +\mathstrut 206232q^{7} \) \(\mathstrut +\mathstrut 1076872q^{8} \) \(\mathstrut -\mathstrut 3319093q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 860q^{3} \) \(\mathstrut -\mathstrut 8556q^{4} \) \(\mathstrut +\mathstrut 14146q^{5} \) \(\mathstrut +\mathstrut 58444q^{6} \) \(\mathstrut +\mathstrut 206232q^{7} \) \(\mathstrut +\mathstrut 1076872q^{8} \) \(\mathstrut -\mathstrut 3319093q^{9} \) \(\mathstrut -\mathstrut 7752648q^{10} \) \(\mathstrut +\mathstrut 9989716q^{11} \) \(\mathstrut -\mathstrut 8536664q^{12} \) \(\mathstrut -\mathstrut 3843462q^{13} \) \(\mathstrut +\mathstrut 21101872q^{14} \) \(\mathstrut +\mathstrut 42509064q^{15} \) \(\mathstrut -\mathstrut 62847216q^{16} \) \(\mathstrut -\mathstrut 227240498q^{17} \) \(\mathstrut +\mathstrut 262778834q^{18} \) \(\mathstrut +\mathstrut 206597196q^{19} \) \(\mathstrut +\mathstrut 381237904q^{20} \) \(\mathstrut -\mathstrut 1370300832q^{21} \) \(\mathstrut +\mathstrut 196775484q^{22} \) \(\mathstrut +\mathstrut 1490018760q^{23} \) \(\mathstrut +\mathstrut 1739438480q^{24} \) \(\mathstrut -\mathstrut 4205723223q^{25} \) \(\mathstrut -\mathstrut 685452248q^{26} \) \(\mathstrut +\mathstrut 5792047640q^{27} \) \(\mathstrut -\mathstrut 978617568q^{28} \) \(\mathstrut -\mathstrut 3556537878q^{29} \) \(\mathstrut +\mathstrut 539961392q^{30} \) \(\mathstrut -\mathstrut 7367666592q^{31} \) \(\mathstrut -\mathstrut 8956909792q^{32} \) \(\mathstrut +\mathstrut 14055767168q^{33} \) \(\mathstrut +\mathstrut 8857451100q^{34} \) \(\mathstrut -\mathstrut 15413225904q^{35} \) \(\mathstrut +\mathstrut 18075363660q^{36} \) \(\mathstrut +\mathstrut 6628831266q^{37} \) \(\mathstrut -\mathstrut 23710846420q^{38} \) \(\mathstrut +\mathstrut 20630243496q^{39} \) \(\mathstrut -\mathstrut 6505554528q^{40} \) \(\mathstrut +\mathstrut 47965956118q^{41} \) \(\mathstrut -\mathstrut 3443304224q^{42} \) \(\mathstrut -\mathstrut 46788121548q^{43} \) \(\mathstrut -\mathstrut 28647791928q^{44} \) \(\mathstrut +\mathstrut 107010747322q^{45} \) \(\mathstrut -\mathstrut 51061300848q^{46} \) \(\mathstrut -\mathstrut 201450140016q^{47} \) \(\mathstrut -\mathstrut 161587694304q^{48} \) \(\mathstrut +\mathstrut 101164221495q^{49} \) \(\mathstrut +\mathstrut 246819442102q^{50} \) \(\mathstrut +\mathstrut 177530164600q^{51} \) \(\mathstrut +\mathstrut 441779820720q^{52} \) \(\mathstrut -\mathstrut 125287225454q^{53} \) \(\mathstrut -\mathstrut 639572716168q^{54} \) \(\mathstrut +\mathstrut 217008668376q^{55} \) \(\mathstrut -\mathstrut 699100837568q^{56} \) \(\mathstrut -\mathstrut 1007795333472q^{57} \) \(\mathstrut +\mathstrut 992195908104q^{58} \) \(\mathstrut +\mathstrut 793560430372q^{59} \) \(\mathstrut +\mathstrut 1614284565792q^{60} \) \(\mathstrut -\mathstrut 698520953142q^{61} \) \(\mathstrut -\mathstrut 1019628353344q^{62} \) \(\mathstrut -\mathstrut 426693206408q^{63} \) \(\mathstrut -\mathstrut 1464077986752q^{64} \) \(\mathstrut -\mathstrut 357709159492q^{65} \) \(\mathstrut +\mathstrut 2946347707608q^{66} \) \(\mathstrut +\mathstrut 1645513736988q^{67} \) \(\mathstrut +\mathstrut 2850998874984q^{68} \) \(\mathstrut +\mathstrut 1015234563872q^{69} \) \(\mathstrut -\mathstrut 5505591528768q^{70} \) \(\mathstrut -\mathstrut 4320352976296q^{71} \) \(\mathstrut -\mathstrut 8538615449032q^{72} \) \(\mathstrut +\mathstrut 3510289845750q^{73} \) \(\mathstrut +\mathstrut 9399657781240q^{74} \) \(\mathstrut +\mathstrut 844579119460q^{75} \) \(\mathstrut +\mathstrut 10892359157736q^{76} \) \(\mathstrut +\mathstrut 1067266262304q^{77} \) \(\mathstrut -\mathstrut 16235130104944q^{78} \) \(\mathstrut -\mathstrut 1836704085264q^{79} \) \(\mathstrut -\mathstrut 16787669526720q^{80} \) \(\mathstrut +\mathstrut 3452732525415q^{81} \) \(\mathstrut +\mathstrut 14910525285612q^{82} \) \(\mathstrut +\mathstrut 3890337600524q^{83} \) \(\mathstrut +\mathstrut 26784826987072q^{84} \) \(\mathstrut +\mathstrut 1613607983652q^{85} \) \(\mathstrut -\mathstrut 24718490913284q^{86} \) \(\mathstrut -\mathstrut 14659545283608q^{87} \) \(\mathstrut -\mathstrut 26046521626416q^{88} \) \(\mathstrut -\mathstrut 745298334170q^{89} \) \(\mathstrut +\mathstrut 43218339424520q^{90} \) \(\mathstrut +\mathstrut 19047242532624q^{91} \) \(\mathstrut +\mathstrut 34108342295904q^{92} \) \(\mathstrut -\mathstrut 6946080702080q^{93} \) \(\mathstrut -\mathstrut 37727942061792q^{94} \) \(\mathstrut -\mathstrut 25493775576920q^{95} \) \(\mathstrut -\mathstrut 62733552180160q^{96} \) \(\mathstrut -\mathstrut 15392053442370q^{97} \) \(\mathstrut +\mathstrut 61714328751438q^{98} \) \(\mathstrut +\mathstrut 42866396476420q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

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
8.14.a \(\chi_{8}(1, \cdot)\) 8.14.a.a 1 1
8.14.a.b 2
8.14.b \(\chi_{8}(5, \cdot)\) 8.14.b.a 2 1
8.14.b.b 10

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

\( S_{14}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)