## Defining parameters

 Level: $$N$$ = $$22 = 2 \cdot 11$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$2$$ Newform subspaces: $$6$$ Sturm bound: $$180$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(22))$$.

Total New Old
Modular forms 85 25 60
Cusp forms 65 25 40
Eisenstein series 20 0 20

## Trace form

 $$25 q + 20 q^{6} - 590 q^{7} + 1100 q^{9} + O(q^{10})$$ $$25 q + 20 q^{6} - 590 q^{7} + 1100 q^{9} + 1000 q^{10} + 890 q^{11} + 160 q^{12} - 1010 q^{13} - 2200 q^{14} - 6490 q^{15} - 800 q^{17} + 4820 q^{18} + 2235 q^{19} + 8820 q^{21} + 17700 q^{23} + 320 q^{24} - 19360 q^{25} - 16720 q^{26} - 33495 q^{27} - 3040 q^{28} - 2140 q^{29} + 16680 q^{30} + 33990 q^{31} + 5120 q^{32} + 55495 q^{33} + 15280 q^{34} + 4060 q^{35} - 880 q^{36} - 15620 q^{37} - 40920 q^{38} - 56230 q^{39} - 19840 q^{40} - 39580 q^{41} + 26840 q^{42} + 53730 q^{43} + 5680 q^{44} + 22250 q^{45} - 52400 q^{46} - 66880 q^{47} - 48400 q^{49} + 7120 q^{50} + 45445 q^{51} + 41920 q^{52} + 92510 q^{53} + 116640 q^{54} + 44950 q^{55} - 31575 q^{57} + 33440 q^{58} - 65395 q^{59} - 31680 q^{60} + 38890 q^{61} - 21240 q^{62} - 92120 q^{63} - 114740 q^{65} - 286160 q^{66} + 15850 q^{67} - 12800 q^{68} + 95370 q^{69} + 125840 q^{70} - 39600 q^{71} + 39680 q^{72} + 19560 q^{73} + 92080 q^{74} + 191455 q^{75} + 57760 q^{76} - 164700 q^{77} + 206560 q^{78} + 89770 q^{79} + 28160 q^{80} + 670395 q^{81} + 122540 q^{82} + 113285 q^{83} - 177920 q^{84} - 515790 q^{85} - 567820 q^{86} - 937100 q^{87} - 95360 q^{88} - 461380 q^{89} - 510360 q^{90} + 10780 q^{91} - 5280 q^{92} + 541970 q^{93} + 453440 q^{94} + 719510 q^{95} - 42185 q^{97} + 432180 q^{98} + 265450 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(22))$$

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
22.6.a $$\chi_{22}(1, \cdot)$$ 22.6.a.a 1 1
22.6.a.b 1
22.6.a.c 1
22.6.a.d 2
22.6.c $$\chi_{22}(3, \cdot)$$ 22.6.c.a 8 4
22.6.c.b 12

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(22))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(22)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$