## Defining parameters

 Level: $$N$$ = $$14\( 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

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