# Properties

 Label 2015.2.cr Level 2015 Weight 2 Character orbit cr Rep. character $$\chi_{2015}(6,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 600 Sturm bound 448

# Learn more about

## Defining parameters

 Level: $$N$$ = $$2015 = 5 \cdot 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 2015.cr (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{12})$$ Sturm bound: $$448$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2015, [\chi])$$.

Total New Old
Modular forms 912 600 312
Cusp forms 880 600 280
Eisenstein series 32 0 32

## Trace form

 $$600q - 28q^{7} - 12q^{8} - 608q^{9} + O(q^{10})$$ $$600q - 28q^{7} - 12q^{8} - 608q^{9} + 12q^{11} - 16q^{12} + 24q^{14} + 312q^{16} - 12q^{17} + 44q^{18} - 8q^{19} + 8q^{20} + 44q^{21} + 72q^{24} - 24q^{26} + 64q^{28} + 24q^{29} + 32q^{31} + 28q^{32} + 32q^{33} - 108q^{34} - 36q^{36} - 28q^{37} + 12q^{39} + 4q^{41} - 64q^{43} - 12q^{44} - 8q^{45} - 48q^{46} - 48q^{47} + 180q^{49} - 24q^{51} - 152q^{52} - 72q^{53} + 92q^{57} + 84q^{58} - 72q^{61} + 36q^{62} + 140q^{63} - 88q^{66} - 60q^{67} - 72q^{69} - 8q^{70} - 88q^{71} - 64q^{72} - 52q^{73} + 120q^{74} - 4q^{75} - 16q^{76} + 64q^{78} + 72q^{79} + 16q^{80} + 536q^{81} + 16q^{84} + 24q^{86} + 8q^{87} - 60q^{88} - 72q^{89} - 68q^{91} + 28q^{93} - 16q^{94} + 300q^{96} + 52q^{97} + 116q^{98} - 60q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2015, [\chi])$$ into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(2015, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2015, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(403, [\chi])$$$$^{\oplus 2}$$