# Properties

 Label 276.2.m Level $276$ Weight $2$ Character orbit 276.m Rep. character $\chi_{276}(7,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $240$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 276.m (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(276, [\chi])$$.

Total New Old
Modular forms 520 240 280
Cusp forms 440 240 200
Eisenstein series 80 0 80

## Trace form

 $$240q - 4q^{2} - 4q^{6} - 4q^{8} + 24q^{9} + O(q^{10})$$ $$240q - 4q^{2} - 4q^{6} - 4q^{8} + 24q^{9} - 8q^{16} + 4q^{18} + 4q^{24} + 24q^{25} - 40q^{26} + 32q^{29} + 36q^{32} - 22q^{34} - 22q^{36} - 110q^{38} - 22q^{40} - 16q^{41} - 110q^{42} - 154q^{44} - 88q^{46} - 56q^{48} - 40q^{49} - 142q^{50} - 70q^{52} - 18q^{54} - 110q^{56} - 46q^{58} - 22q^{60} + 40q^{62} - 48q^{64} - 16q^{69} - 72q^{70} + 4q^{72} + 22q^{74} + 110q^{76} - 192q^{77} + 198q^{80} - 24q^{81} + 172q^{82} - 200q^{85} + 220q^{86} + 176q^{88} - 88q^{89} + 154q^{92} - 16q^{93} + 126q^{94} - 44q^{96} - 88q^{97} + 228q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(276, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
276.2.m.a $$240$$ $$2.204$$ None $$-4$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(276, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(276, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 2}$$