Properties

Label 14.4
Level 14
Weight 4
Dimension 6
Nonzero newspaces 2
Newforms 4
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(14))\).

Total New Old
Modular forms 24 6 18
Cusp forms 12 6 6
Eisenstein series 12 0 12

Trace form

\(6q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 36q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 36q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut +\mathstrut 42q^{9} \) \(\mathstrut +\mathstrut 36q^{10} \) \(\mathstrut +\mathstrut 42q^{11} \) \(\mathstrut +\mathstrut 48q^{12} \) \(\mathstrut +\mathstrut 66q^{13} \) \(\mathstrut +\mathstrut 132q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut -\mathstrut 150q^{17} \) \(\mathstrut -\mathstrut 168q^{18} \) \(\mathstrut -\mathstrut 60q^{19} \) \(\mathstrut -\mathstrut 120q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 216q^{22} \) \(\mathstrut -\mathstrut 294q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 210q^{25} \) \(\mathstrut +\mathstrut 348q^{26} \) \(\mathstrut +\mathstrut 576q^{27} \) \(\mathstrut +\mathstrut 120q^{28} \) \(\mathstrut +\mathstrut 576q^{29} \) \(\mathstrut +\mathstrut 168q^{30} \) \(\mathstrut +\mathstrut 210q^{31} \) \(\mathstrut -\mathstrut 570q^{33} \) \(\mathstrut -\mathstrut 408q^{34} \) \(\mathstrut -\mathstrut 420q^{35} \) \(\mathstrut -\mathstrut 168q^{36} \) \(\mathstrut +\mathstrut 42q^{37} \) \(\mathstrut +\mathstrut 108q^{38} \) \(\mathstrut -\mathstrut 252q^{39} \) \(\mathstrut +\mathstrut 144q^{40} \) \(\mathstrut -\mathstrut 792q^{41} \) \(\mathstrut +\mathstrut 324q^{42} \) \(\mathstrut -\mathstrut 516q^{43} \) \(\mathstrut +\mathstrut 168q^{44} \) \(\mathstrut -\mathstrut 78q^{45} \) \(\mathstrut -\mathstrut 168q^{46} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut -\mathstrut 96q^{48} \) \(\mathstrut -\mathstrut 90q^{49} \) \(\mathstrut +\mathstrut 24q^{50} \) \(\mathstrut +\mathstrut 1134q^{51} \) \(\mathstrut +\mathstrut 312q^{52} \) \(\mathstrut +\mathstrut 1302q^{53} \) \(\mathstrut -\mathstrut 144q^{54} \) \(\mathstrut +\mathstrut 1332q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 312q^{57} \) \(\mathstrut -\mathstrut 504q^{58} \) \(\mathstrut -\mathstrut 264q^{59} \) \(\mathstrut -\mathstrut 504q^{60} \) \(\mathstrut +\mathstrut 840q^{61} \) \(\mathstrut +\mathstrut 120q^{62} \) \(\mathstrut -\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 384q^{64} \) \(\mathstrut -\mathstrut 2016q^{65} \) \(\mathstrut -\mathstrut 384q^{66} \) \(\mathstrut -\mathstrut 2058q^{67} \) \(\mathstrut -\mathstrut 600q^{68} \) \(\mathstrut -\mathstrut 1332q^{69} \) \(\mathstrut -\mathstrut 756q^{70} \) \(\mathstrut -\mathstrut 792q^{71} \) \(\mathstrut -\mathstrut 672q^{72} \) \(\mathstrut -\mathstrut 594q^{73} \) \(\mathstrut +\mathstrut 1512q^{74} \) \(\mathstrut +\mathstrut 234q^{75} \) \(\mathstrut +\mathstrut 1464q^{76} \) \(\mathstrut +\mathstrut 2226q^{77} \) \(\mathstrut +\mathstrut 1152q^{78} \) \(\mathstrut +\mathstrut 1050q^{79} \) \(\mathstrut -\mathstrut 384q^{80} \) \(\mathstrut +\mathstrut 84q^{81} \) \(\mathstrut -\mathstrut 984q^{82} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 912q^{84} \) \(\mathstrut +\mathstrut 240q^{85} \) \(\mathstrut +\mathstrut 840q^{86} \) \(\mathstrut +\mathstrut 2304q^{87} \) \(\mathstrut +\mathstrut 1344q^{88} \) \(\mathstrut +\mathstrut 2310q^{89} \) \(\mathstrut +\mathstrut 2388q^{90} \) \(\mathstrut +\mathstrut 906q^{91} \) \(\mathstrut -\mathstrut 432q^{92} \) \(\mathstrut +\mathstrut 294q^{93} \) \(\mathstrut -\mathstrut 816q^{94} \) \(\mathstrut -\mathstrut 2058q^{95} \) \(\mathstrut -\mathstrut 192q^{96} \) \(\mathstrut -\mathstrut 4224q^{97} \) \(\mathstrut -\mathstrut 2640q^{98} \) \(\mathstrut -\mathstrut 3732q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.4.a \(\chi_{14}(1, \cdot)\) 14.4.a.a 1 1
14.4.a.b 1
14.4.c \(\chi_{14}(9, \cdot)\) 14.4.c.a 2 2
14.4.c.b 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)