Properties

Label 8.13
Level 8
Weight 13
Dimension 11
Nonzero newspaces 1
Newforms 2
Sturm bound 52
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(52\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(8))\).

Total New Old
Modular forms 27 13 14
Cusp forms 21 11 10
Eisenstein series 6 2 4

Trace form

\(11q \) \(\mathstrut -\mathstrut 46q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 1652q^{4} \) \(\mathstrut -\mathstrut 88676q^{6} \) \(\mathstrut +\mathstrut 289304q^{8} \) \(\mathstrut +\mathstrut 1594321q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11q \) \(\mathstrut -\mathstrut 46q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 1652q^{4} \) \(\mathstrut -\mathstrut 88676q^{6} \) \(\mathstrut +\mathstrut 289304q^{8} \) \(\mathstrut +\mathstrut 1594321q^{9} \) \(\mathstrut +\mathstrut 1873200q^{10} \) \(\mathstrut -\mathstrut 2668322q^{11} \) \(\mathstrut -\mathstrut 2732552q^{12} \) \(\mathstrut +\mathstrut 12728736q^{14} \) \(\mathstrut -\mathstrut 21516784q^{16} \) \(\mathstrut -\mathstrut 2419562q^{17} \) \(\mathstrut +\mathstrut 1926742q^{18} \) \(\mathstrut -\mathstrut 51868610q^{19} \) \(\mathstrut +\mathstrut 17615520q^{20} \) \(\mathstrut -\mathstrut 103924772q^{22} \) \(\mathstrut +\mathstrut 341593744q^{24} \) \(\mathstrut -\mathstrut 462805765q^{25} \) \(\mathstrut +\mathstrut 151295184q^{26} \) \(\mathstrut +\mathstrut 967927996q^{27} \) \(\mathstrut -\mathstrut 132075840q^{28} \) \(\mathstrut +\mathstrut 456064800q^{30} \) \(\mathstrut -\mathstrut 1577462176q^{32} \) \(\mathstrut +\mathstrut 787396076q^{33} \) \(\mathstrut +\mathstrut 1555715044q^{34} \) \(\mathstrut -\mathstrut 2838470400q^{35} \) \(\mathstrut -\mathstrut 4478101220q^{36} \) \(\mathstrut -\mathstrut 3983433572q^{38} \) \(\mathstrut +\mathstrut 8180322240q^{40} \) \(\mathstrut -\mathstrut 3710988362q^{41} \) \(\mathstrut +\mathstrut 14692585920q^{42} \) \(\mathstrut +\mathstrut 18050876638q^{43} \) \(\mathstrut -\mathstrut 20073482120q^{44} \) \(\mathstrut -\mathstrut 16813594656q^{46} \) \(\mathstrut +\mathstrut 24349522528q^{48} \) \(\mathstrut -\mathstrut 25691199637q^{49} \) \(\mathstrut +\mathstrut 40513425650q^{50} \) \(\mathstrut +\mathstrut 6952490492q^{51} \) \(\mathstrut -\mathstrut 36172521120q^{52} \) \(\mathstrut -\mathstrut 100535014088q^{54} \) \(\mathstrut +\mathstrut 154450364544q^{56} \) \(\mathstrut +\mathstrut 22549744556q^{57} \) \(\mathstrut +\mathstrut 193270394640q^{58} \) \(\mathstrut -\mathstrut 100809712226q^{59} \) \(\mathstrut -\mathstrut 347360715840q^{60} \) \(\mathstrut -\mathstrut 299237961600q^{62} \) \(\mathstrut +\mathstrut 344932668992q^{64} \) \(\mathstrut +\mathstrut 96485235840q^{65} \) \(\mathstrut +\mathstrut 567267337352q^{66} \) \(\mathstrut +\mathstrut 125184923518q^{67} \) \(\mathstrut -\mathstrut 482345621912q^{68} \) \(\mathstrut -\mathstrut 799057954560q^{70} \) \(\mathstrut +\mathstrut 1051757829832q^{72} \) \(\mathstrut -\mathstrut 9696103562q^{73} \) \(\mathstrut +\mathstrut 742739480496q^{74} \) \(\mathstrut -\mathstrut 91148212130q^{75} \) \(\mathstrut -\mathstrut 1059904664072q^{76} \) \(\mathstrut -\mathstrut 1795838526240q^{78} \) \(\mathstrut +\mathstrut 1981932232320q^{80} \) \(\mathstrut +\mathstrut 39118873879q^{81} \) \(\mathstrut +\mathstrut 2206318374628q^{82} \) \(\mathstrut -\mathstrut 339177211202q^{83} \) \(\mathstrut -\mathstrut 3144240693120q^{84} \) \(\mathstrut -\mathstrut 2711857667492q^{86} \) \(\mathstrut +\mathstrut 2674492705168q^{88} \) \(\mathstrut +\mathstrut 47015069110q^{89} \) \(\mathstrut +\mathstrut 3983485096080q^{90} \) \(\mathstrut +\mathstrut 361546645248q^{91} \) \(\mathstrut -\mathstrut 2649411172800q^{92} \) \(\mathstrut -\mathstrut 2517413216064q^{94} \) \(\mathstrut +\mathstrut 3543110668864q^{96} \) \(\mathstrut +\mathstrut 182261693398q^{97} \) \(\mathstrut +\mathstrut 3263732873234q^{98} \) \(\mathstrut -\mathstrut 906543916678q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(8))\)

We only show spaces with odd 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
8.13.c \(\chi_{8}(7, \cdot)\) None 0 1
8.13.d \(\chi_{8}(3, \cdot)\) 8.13.d.a 1 1
8.13.d.b 10

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)