Properties

Label 14.6
Level 14
Weight 6
Dimension 10
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 72
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(14))\).

Total New Old
Modular forms 36 10 26
Cusp forms 24 10 14
Eisenstein series 12 0 12

Trace form

\( 10 q + 18 q^{3} - 32 q^{4} + 66 q^{5} + 216 q^{6} + 232 q^{7} - 1218 q^{9} + O(q^{10}) \) \( 10 q + 18 q^{3} - 32 q^{4} + 66 q^{5} + 216 q^{6} + 232 q^{7} - 1218 q^{9} - 744 q^{10} - 444 q^{11} + 288 q^{12} + 3650 q^{13} - 120 q^{14} - 2568 q^{15} - 512 q^{16} - 3228 q^{17} + 1488 q^{18} + 3518 q^{19} + 2400 q^{20} + 8790 q^{21} + 2832 q^{22} - 2112 q^{23} - 1920 q^{24} - 38 q^{25} - 11352 q^{26} - 24372 q^{27} - 6656 q^{28} - 4248 q^{29} + 6288 q^{30} + 18956 q^{31} + 8844 q^{33} + 13872 q^{34} - 10878 q^{35} + 23520 q^{36} + 27476 q^{37} - 1224 q^{38} - 12840 q^{39} - 11904 q^{40} - 6336 q^{41} - 57384 q^{42} - 29308 q^{43} - 7104 q^{44} + 26742 q^{45} + 46320 q^{46} + 38196 q^{47} + 4608 q^{48} + 58570 q^{49} + 65616 q^{50} - 40140 q^{51} - 22240 q^{52} - 90840 q^{53} - 89568 q^{54} - 50328 q^{55} - 21120 q^{56} - 99468 q^{57} - 28368 q^{58} - 31098 q^{59} + 42624 q^{60} + 110474 q^{61} + 161904 q^{62} + 229020 q^{63} + 40960 q^{64} + 14868 q^{65} - 96000 q^{66} + 65504 q^{67} - 51648 q^{68} - 33336 q^{69} - 131208 q^{70} - 135720 q^{71} + 23808 q^{72} - 46048 q^{73} + 36720 q^{74} + 110310 q^{75} + 26720 q^{76} + 4368 q^{77} + 182016 q^{78} - 82672 q^{79} + 16896 q^{80} - 103470 q^{81} - 128208 q^{82} - 64770 q^{83} - 69792 q^{84} - 157548 q^{85} + 63696 q^{86} + 220428 q^{87} - 23040 q^{88} - 29064 q^{89} - 64392 q^{90} - 134530 q^{91} - 38016 q^{92} + 25020 q^{93} + 47328 q^{94} - 93984 q^{95} - 30720 q^{96} - 100264 q^{97} - 50016 q^{98} + 667740 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.6.a \(\chi_{14}(1, \cdot)\) 14.6.a.a 1 1
14.6.a.b 1
14.6.c \(\chi_{14}(9, \cdot)\) 14.6.c.a 4 2
14.6.c.b 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)