Properties

Label 14.14
Level 14
Weight 14
Dimension 22
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 84 22 62
Cusp forms 72 22 50
Eisenstein series 12 0 12

Trace form

\( 22q + 2658q^{3} - 8192q^{4} + 12846q^{5} - 113280q^{6} - 382088q^{7} - 3438246q^{9} + O(q^{10}) \) \( 22q + 2658q^{3} - 8192q^{4} + 12846q^{5} - 113280q^{6} - 382088q^{7} - 3438246q^{9} + 1155456q^{10} - 13934604q^{11} + 10887168q^{12} + 33708770q^{13} + 35452032q^{14} - 151109688q^{15} - 33554432q^{16} - 45572208q^{17} - 183558912q^{18} - 282822898q^{19} + 821944320q^{20} - 513157806q^{21} - 1416976128q^{22} + 2808150888q^{23} - 750256128q^{24} - 996371738q^{25} - 1887563136q^{26} - 10681505172q^{27} + 1788903424q^{28} + 11758821408q^{29} + 2408656128q^{30} - 9271633756q^{31} + 4313374584q^{33} + 17188135680q^{34} + 36911769762q^{35} + 27498455040q^{36} - 29593228264q^{37} - 34253357184q^{38} - 71382226392q^{39} + 4732747776q^{40} + 263744467848q^{41} + 30614295936q^{42} - 278396849068q^{43} - 57076137984q^{44} - 162333777138q^{45} + 17435425536q^{46} + 288153063036q^{47} + 44593840128q^{48} + 173173682710q^{49} - 231469665024q^{50} - 495671494140q^{51} - 201358336000q^{52} - 18582101220q^{53} + 747862728192q^{54} + 1194171358392q^{55} - 21150302208q^{56} - 1540320102948q^{57} - 715506486528q^{58} - 1773080057082q^{59} + 768137232384q^{60} + 1471912187606q^{61} + 393014025984q^{62} + 3622004475180q^{63} + 1511828488192q^{64} - 5013396201492q^{65} - 4550836752384q^{66} - 1885715579056q^{67} - 186663763968q^{68} + 11222669299536q^{69} + 3403106646912q^{70} - 305143351848q^{71} - 751857303552q^{72} - 7853502854308q^{73} - 3784216506624q^{74} + 2598390629190q^{75} + 6694973038592q^{76} + 11432830921428q^{77} - 5309188091904q^{78} - 11736575665336q^{79} + 215520116736q^{80} - 2933505361806q^{81} + 440078045952q^{82} + 887075655150q^{83} - 1208568668160q^{84} - 2124437327028q^{85} - 302497813248q^{86} - 9755550406692q^{87} + 265845473280q^{88} + 12796077806484q^{89} + 8598252978048q^{90} + 3187518646046q^{91} + 8745915285504q^{92} - 42999902503680q^{93} - 14473100262912q^{94} + 36159401606376q^{95} - 3073049100288q^{96} - 425201807104q^{97} - 2608265565696q^{98} - 11854055341428q^{99} + O(q^{100}) \)

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

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
14.14.a \(\chi_{14}(1, \cdot)\) 14.14.a.a 1 1
14.14.a.b 1
14.14.a.c 2
14.14.a.d 2
14.14.c \(\chi_{14}(9, \cdot)\) 14.14.c.a 8 2
14.14.c.b 8

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

\( S_{14}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)