Properties

Label 13.7
Level 13
Weight 7
Dimension 36
Nonzero newspaces 2
Newforms 2
Sturm bound 98
Trace bound 1

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(98\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(13))\).

Total New Old
Modular forms 48 48 0
Cusp forms 36 36 0
Eisenstein series 12 12 0

Trace form

\(36q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 714q^{7} \) \(\mathstrut -\mathstrut 2310q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(36q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 714q^{7} \) \(\mathstrut -\mathstrut 2310q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 4674q^{10} \) \(\mathstrut +\mathstrut 1914q^{11} \) \(\mathstrut -\mathstrut 5478q^{13} \) \(\mathstrut -\mathstrut 9132q^{14} \) \(\mathstrut -\mathstrut 7782q^{15} \) \(\mathstrut -\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 20898q^{17} \) \(\mathstrut +\mathstrut 9624q^{18} \) \(\mathstrut -\mathstrut 12270q^{19} \) \(\mathstrut -\mathstrut 33678q^{20} \) \(\mathstrut +\mathstrut 3114q^{21} \) \(\mathstrut +\mathstrut 66684q^{22} \) \(\mathstrut +\mathstrut 29634q^{23} \) \(\mathstrut +\mathstrut 78762q^{24} \) \(\mathstrut -\mathstrut 57756q^{26} \) \(\mathstrut -\mathstrut 127524q^{27} \) \(\mathstrut -\mathstrut 36480q^{28} \) \(\mathstrut -\mathstrut 89082q^{29} \) \(\mathstrut -\mathstrut 247734q^{30} \) \(\mathstrut -\mathstrut 57102q^{31} \) \(\mathstrut +\mathstrut 115944q^{32} \) \(\mathstrut +\mathstrut 261594q^{33} \) \(\mathstrut +\mathstrut 361794q^{34} \) \(\mathstrut +\mathstrut 263634q^{35} \) \(\mathstrut +\mathstrut 105066q^{36} \) \(\mathstrut -\mathstrut 71682q^{37} \) \(\mathstrut +\mathstrut 166362q^{39} \) \(\mathstrut -\mathstrut 379524q^{40} \) \(\mathstrut -\mathstrut 547632q^{41} \) \(\mathstrut -\mathstrut 984840q^{42} \) \(\mathstrut -\mathstrut 480486q^{43} \) \(\mathstrut -\mathstrut 308340q^{44} \) \(\mathstrut +\mathstrut 312804q^{45} \) \(\mathstrut +\mathstrut 967638q^{46} \) \(\mathstrut +\mathstrut 702474q^{47} \) \(\mathstrut +\mathstrut 1606410q^{48} \) \(\mathstrut +\mathstrut 854562q^{49} \) \(\mathstrut +\mathstrut 839136q^{50} \) \(\mathstrut -\mathstrut 1350204q^{52} \) \(\mathstrut -\mathstrut 887940q^{53} \) \(\mathstrut -\mathstrut 2142480q^{54} \) \(\mathstrut -\mathstrut 1469526q^{55} \) \(\mathstrut -\mathstrut 1461108q^{56} \) \(\mathstrut -\mathstrut 543486q^{57} \) \(\mathstrut +\mathstrut 113826q^{58} \) \(\mathstrut +\mathstrut 573594q^{59} \) \(\mathstrut +\mathstrut 3294612q^{60} \) \(\mathstrut +\mathstrut 1782372q^{61} \) \(\mathstrut +\mathstrut 3741966q^{62} \) \(\mathstrut +\mathstrut 2202042q^{63} \) \(\mathstrut -\mathstrut 2077032q^{65} \) \(\mathstrut -\mathstrut 5495280q^{66} \) \(\mathstrut -\mathstrut 2932278q^{67} \) \(\mathstrut -\mathstrut 2882184q^{68} \) \(\mathstrut -\mathstrut 1475766q^{69} \) \(\mathstrut +\mathstrut 332412q^{70} \) \(\mathstrut +\mathstrut 1481082q^{71} \) \(\mathstrut +\mathstrut 3080544q^{72} \) \(\mathstrut +\mathstrut 2914554q^{73} \) \(\mathstrut +\mathstrut 5533470q^{74} \) \(\mathstrut +\mathstrut 3466008q^{75} \) \(\mathstrut +\mathstrut 1769142q^{76} \) \(\mathstrut -\mathstrut 1496064q^{78} \) \(\mathstrut -\mathstrut 1809660q^{79} \) \(\mathstrut -\mathstrut 7899708q^{80} \) \(\mathstrut -\mathstrut 4789212q^{81} \) \(\mathstrut -\mathstrut 3540426q^{82} \) \(\mathstrut -\mathstrut 2747166q^{83} \) \(\mathstrut -\mathstrut 268140q^{84} \) \(\mathstrut +\mathstrut 3615312q^{85} \) \(\mathstrut +\mathstrut 3572508q^{86} \) \(\mathstrut +\mathstrut 2640762q^{87} \) \(\mathstrut +\mathstrut 4478052q^{88} \) \(\mathstrut -\mathstrut 344622q^{89} \) \(\mathstrut -\mathstrut 1858038q^{91} \) \(\mathstrut +\mathstrut 2026812q^{92} \) \(\mathstrut -\mathstrut 511782q^{93} \) \(\mathstrut -\mathstrut 4686090q^{94} \) \(\mathstrut -\mathstrut 2753718q^{95} \) \(\mathstrut -\mathstrut 3082824q^{96} \) \(\mathstrut +\mathstrut 3241602q^{97} \) \(\mathstrut +\mathstrut 6023610q^{98} \) \(\mathstrut +\mathstrut 7231194q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.7.d \(\chi_{13}(5, \cdot)\) 13.7.d.a 12 2
13.7.f \(\chi_{13}(2, \cdot)\) 13.7.f.a 24 4