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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

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

Display 100 coefficients 10 coefficients

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

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