## Defining parameters

 Level: $$N$$ = $$14 = 2 \cdot 7$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$2$$ Newform subspaces: $$4$$ 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

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

## 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

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