# Properties

 Label 276.2.a Level $276$ Weight $2$ Character orbit 276.a Rep. character $\chi_{276}(1,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 276.a (trivial) Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(276))$$.

Total New Old
Modular forms 54 4 50
Cusp forms 43 4 39
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$$$3$$$$23$$FrickeDim.
$$-$$$$+$$$$+$$$$-$$$$2$$
$$-$$$$-$$$$-$$$$-$$$$2$$
Plus space$$+$$$$0$$
Minus space$$-$$$$4$$

## Trace form

 $$4q + 4q^{5} + 4q^{7} + 4q^{9} + O(q^{10})$$ $$4q + 4q^{5} + 4q^{7} + 4q^{9} + 8q^{13} + 4q^{15} + 12q^{17} - 4q^{19} - 4q^{21} + 12q^{25} + 16q^{29} - 8q^{31} - 16q^{35} - 16q^{37} - 8q^{39} - 8q^{41} - 12q^{43} + 4q^{45} - 16q^{47} + 4q^{49} - 4q^{51} + 4q^{53} - 16q^{55} - 12q^{57} - 16q^{59} + 4q^{63} - 16q^{65} - 28q^{67} + 4q^{69} + 8q^{73} - 8q^{75} - 16q^{77} + 20q^{79} + 4q^{81} - 16q^{83} + 8q^{87} + 12q^{89} - 8q^{93} + 16q^{95} - 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(276))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2 3 23
276.2.a.a $$2$$ $$2.204$$ $$\Q(\sqrt{10})$$ None $$0$$ $$-2$$ $$0$$ $$4$$ $$-$$ $$+$$ $$+$$ $$q-q^{3}+\beta q^{5}+(2-\beta )q^{7}+q^{9}+4q^{13}+\cdots$$
276.2.a.b $$2$$ $$2.204$$ $$\Q(\sqrt{2})$$ None $$0$$ $$2$$ $$4$$ $$0$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}+(2+\beta )q^{5}+\beta q^{7}+q^{9}-4\beta q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(276))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(276)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(69))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(92))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(138))$$$$^{\oplus 2}$$