## Defining parameters

 Level: $$N$$ = $$547$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$10$$ Sturm bound: $$49868$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(547))$$.

Total New Old
Modular forms 12740 12740 0
Cusp forms 12195 12195 0
Eisenstein series 545 545 0

## Trace form

 $$12195q - 270q^{2} - 269q^{3} - 266q^{4} - 267q^{5} - 261q^{6} - 265q^{7} - 258q^{8} - 260q^{9} + O(q^{10})$$ $$12195q - 270q^{2} - 269q^{3} - 266q^{4} - 267q^{5} - 261q^{6} - 265q^{7} - 258q^{8} - 260q^{9} - 255q^{10} - 261q^{11} - 245q^{12} - 259q^{13} - 249q^{14} - 249q^{15} - 242q^{16} - 255q^{17} - 234q^{18} - 253q^{19} - 231q^{20} - 241q^{21} - 237q^{22} - 249q^{23} - 213q^{24} - 242q^{25} - 231q^{26} - 233q^{27} - 217q^{28} - 243q^{29} - 201q^{30} - 241q^{31} - 210q^{32} - 225q^{33} - 219q^{34} - 225q^{35} - 182q^{36} - 235q^{37} - 213q^{38} - 217q^{39} - 183q^{40} - 231q^{41} - 177q^{42} - 229q^{43} - 189q^{44} - 195q^{45} - 201q^{46} - 225q^{47} - 149q^{48} - 216q^{49} - 180q^{50} - 201q^{51} - 175q^{52} - 219q^{53} - 153q^{54} - 201q^{55} - 153q^{56} - 193q^{57} - 183q^{58} - 213q^{59} - 105q^{60} - 211q^{61} - 177q^{62} - 169q^{63} - 146q^{64} - 189q^{65} - 129q^{66} - 205q^{67} - 147q^{68} - 177q^{69} - 129q^{70} - 201q^{71} - 78q^{72} - 199q^{73} - 159q^{74} - 149q^{75} - 133q^{76} - 177q^{77} - 105q^{78} - 193q^{79} - 87q^{80} - 152q^{81} - 147q^{82} - 189q^{83} - 49q^{84} - 165q^{85} - 141q^{86} - 153q^{87} - 93q^{88} - 183q^{89} - 39q^{90} - 161q^{91} - 105q^{92} - 145q^{93} - 129q^{94} - 153q^{95} - 21q^{96} - 175q^{97} - 102q^{98} - 117q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(547))$$

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
547.2.a $$\chi_{547}(1, \cdot)$$ 547.2.a.a 2 1
547.2.a.b 18
547.2.a.c 25
547.2.c $$\chi_{547}(40, \cdot)$$ 547.2.c.a 90 2
547.2.e $$\chi_{547}(9, \cdot)$$ 547.2.e.a 264 6
547.2.f $$\chi_{547}(46, \cdot)$$ 547.2.f.a 528 12
547.2.h $$\chi_{547}(13, \cdot)$$ 547.2.h.a 540 12
547.2.j $$\chi_{547}(11, \cdot)$$ 547.2.j.a 1080 24
547.2.m $$\chi_{547}(10, \cdot)$$ 547.2.m.a 3168 72
547.2.o $$\chi_{547}(4, \cdot)$$ 547.2.o.a 6480 144