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Properties

Label 14.10
Level 14
Weight 10
Dimension 16
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(14))\).

Total New Old
Modular forms 60 16 44
Cusp forms 48 16 32
Eisenstein series 12 0 12

Trace form

\( 16 q - 32 q^{2} - 12 q^{3} - 512 q^{4} - 3444 q^{5} + 12768 q^{6} - 1784 q^{7} - 8192 q^{8} + 41388 q^{9} + O(q^{10}) \) \( 16 q - 32 q^{2} - 12 q^{3} - 512 q^{4} - 3444 q^{5} + 12768 q^{6} - 1784 q^{7} - 8192 q^{8} + 41388 q^{9} + 49056 q^{10} + 49506 q^{11} - 3072 q^{12} + 204410 q^{13} - 175904 q^{14} + 624372 q^{15} - 131072 q^{16} - 1171470 q^{17} - 849120 q^{18} + 892100 q^{19} + 514560 q^{20} - 61728 q^{21} + 775488 q^{22} - 6884358 q^{23} - 466944 q^{24} - 2449688 q^{25} - 1334944 q^{26} + 23712624 q^{27} + 3433984 q^{28} - 9160380 q^{29} - 18072192 q^{30} - 12681910 q^{31} - 2097152 q^{32} + 25482786 q^{33} + 23961216 q^{34} + 34021092 q^{35} + 29153280 q^{36} - 84667126 q^{37} - 49294432 q^{38} + 33234684 q^{39} + 12558336 q^{40} + 103079556 q^{41} + 50046432 q^{42} - 106746652 q^{43} + 12673536 q^{44} - 240131598 q^{45} - 41442432 q^{46} + 30612630 q^{47} + 31064064 q^{48} + 189121360 q^{49} - 53004704 q^{50} - 11940930 q^{51} - 37210624 q^{52} + 43182078 q^{53} - 126894528 q^{54} - 42579468 q^{55} + 28696576 q^{56} + 110895672 q^{57} + 94601856 q^{58} + 22747920 q^{59} + 147515904 q^{60} + 196941860 q^{61} + 44818496 q^{62} - 114794616 q^{63} + 268435456 q^{64} - 83308512 q^{65} - 22186752 q^{66} + 270031526 q^{67} - 299896320 q^{68} - 930360780 q^{69} - 590929248 q^{70} + 881132616 q^{71} - 217374720 q^{72} + 723010118 q^{73} + 516837248 q^{74} - 687736950 q^{75} - 418783744 q^{76} - 1135851402 q^{77} + 1155007488 q^{78} + 1119367706 q^{79} - 225705984 q^{80} - 737784798 q^{81} - 1298006784 q^{82} + 12360762 q^{83} - 1169058816 q^{84} - 540605688 q^{85} + 245645504 q^{86} + 332551368 q^{87} + 257310720 q^{88} + 61119390 q^{89} + 3590538528 q^{90} + 1594598498 q^{91} + 1484829696 q^{92} - 919222998 q^{93} - 367048512 q^{94} + 1274394246 q^{95} - 119537664 q^{96} - 4014782740 q^{97} - 2968313888 q^{98} - 981228444 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
14.10.a \(\chi_{14}(1, \cdot)\) 14.10.a.a 1 1
14.10.a.b 1
14.10.a.c 2
14.10.c \(\chi_{14}(9, \cdot)\) 14.10.c.a 6 2
14.10.c.b 6

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)