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

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

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 the 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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + 2 T + 3 T^{2} \)
$5$ \( 1 + 5 T^{2} \)
$7$ \( 1 - T \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 + 4 T + 13 T^{2} \)
$17$ \( 1 - 6 T + 17 T^{2} \)
$19$ \( 1 - 2 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 + 4 T + 31 T^{2} \)
$37$ \( 1 - 2 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 - 8 T + 43 T^{2} \)
$47$ \( 1 + 12 T + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 + 6 T + 59 T^{2} \)
$61$ \( 1 - 8 T + 61 T^{2} \)
$67$ \( 1 + 4 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 - 2 T + 73 T^{2} \)
$79$ \( 1 - 8 T + 79 T^{2} \)
$83$ \( 1 + 6 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 + 10 T + 97 T^{2} \)
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