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Properties

Label 14.2
Level 14
Weight 2
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(14))\).

Total New Old
Modular forms 12 1 11
Cusp forms 1 1 0
Eisenstein series 11 0 11

Trace form

\( q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{12} - 4 q^{13} - q^{14} + q^{16} + 6 q^{17} - q^{18} + 2 q^{19} - 2 q^{21} + 2 q^{24} - 5 q^{25} + 4 q^{26} + 4 q^{27} + q^{28} - 6 q^{29} - 4 q^{31} - q^{32} - 6 q^{34} + q^{36} + 2 q^{37} - 2 q^{38} + 8 q^{39} + 6 q^{41} + 2 q^{42} + 8 q^{43} - 12 q^{47} - 2 q^{48} + q^{49} + 5 q^{50} - 12 q^{51} - 4 q^{52} + 6 q^{53} - 4 q^{54} - q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 8 q^{61} + 4 q^{62} + q^{63} + q^{64} - 4 q^{67} + 6 q^{68} - q^{72} + 2 q^{73} - 2 q^{74} + 10 q^{75} + 2 q^{76} - 8 q^{78} + 8 q^{79} - 11 q^{81} - 6 q^{82} - 6 q^{83} - 2 q^{84} - 8 q^{86} + 12 q^{87} - 6 q^{89} - 4 q^{91} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 10 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.2.a \(\chi_{14}(1, \cdot)\) 14.2.a.a 1 1
14.2.c \(\chi_{14}(9, \cdot)\) None 0 2