## Defining parameters

 Level: $$N$$ = $$2012 = 2^{2} \cdot 503$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Sturm bound: $$506016$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2012))$$.

Total New Old
Modular forms 127759 74296 53463
Cusp forms 125250 73292 51958
Eisenstein series 2509 1004 1505

## Trace form

 $$73292q - 251q^{2} - 251q^{4} - 502q^{5} - 251q^{6} - 251q^{8} - 502q^{9} + O(q^{10})$$ $$73292q - 251q^{2} - 251q^{4} - 502q^{5} - 251q^{6} - 251q^{8} - 502q^{9} - 251q^{10} - 251q^{12} - 502q^{13} - 251q^{14} - 251q^{16} - 502q^{17} - 251q^{18} - 251q^{20} - 502q^{21} - 251q^{22} - 251q^{24} - 502q^{25} - 251q^{26} - 251q^{28} - 502q^{29} - 251q^{30} - 251q^{32} - 502q^{33} - 251q^{34} - 251q^{36} - 502q^{37} - 251q^{38} - 251q^{40} - 502q^{41} - 251q^{42} - 251q^{44} - 502q^{45} - 251q^{46} - 251q^{48} - 502q^{49} - 251q^{50} - 251q^{52} - 502q^{53} - 251q^{54} - 251q^{56} - 502q^{57} - 251q^{58} - 251q^{60} - 502q^{61} - 251q^{62} - 251q^{64} - 502q^{65} - 251q^{66} - 251q^{68} - 502q^{69} - 251q^{70} - 251q^{72} - 502q^{73} - 251q^{74} - 251q^{76} - 502q^{77} - 251q^{78} - 251q^{80} - 502q^{81} - 251q^{82} - 251q^{84} - 502q^{85} - 251q^{86} - 251q^{88} - 502q^{89} - 251q^{90} - 251q^{92} - 502q^{93} - 251q^{94} - 251q^{96} - 502q^{97} - 251q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2012))$$

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
2012.2.a $$\chi_{2012}(1, \cdot)$$ 2012.2.a.a 21 1
2012.2.a.b 21
2012.2.b $$\chi_{2012}(2011, \cdot)$$ n/a 250 1
2012.2.e $$\chi_{2012}(9, \cdot)$$ n/a 10500 250
2012.2.h $$\chi_{2012}(15, \cdot)$$ n/a 62500 250

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2012))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2012)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(503))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1006))$$$$^{\oplus 2}$$