## Defining parameters

 Level: $$N$$ = $$276 = 2^{2} \cdot 3 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$11$$ Sturm bound: $$8448$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(276))$$.

Total New Old
Modular forms 2332 960 1372
Cusp forms 1893 880 1013
Eisenstein series 439 80 359

## Trace form

 $$880q - 22q^{4} - 11q^{6} - 22q^{9} + O(q^{10})$$ $$880q - 22q^{4} - 11q^{6} - 22q^{9} - 22q^{10} - 11q^{12} - 44q^{13} + 11q^{15} - 22q^{16} + 22q^{17} - 11q^{18} + 22q^{19} + 11q^{21} - 44q^{22} + 44q^{23} - 22q^{24} + 33q^{27} - 22q^{28} + 22q^{29} - 11q^{30} + 22q^{31} - 11q^{33} - 66q^{34} - 44q^{35} - 33q^{36} - 132q^{37} - 110q^{38} - 44q^{39} - 198q^{40} - 44q^{41} - 121q^{42} - 88q^{43} - 154q^{44} - 44q^{45} - 198q^{46} - 88q^{47} - 99q^{48} - 176q^{49} - 154q^{50} - 44q^{51} - 242q^{52} - 44q^{53} - 33q^{54} - 88q^{55} - 110q^{56} - 99q^{57} - 132q^{58} - 44q^{59} - 33q^{60} - 44q^{61} - 55q^{63} - 22q^{64} + 22q^{66} - 77q^{69} - 44q^{70} - 11q^{72} - 44q^{73} + 22q^{74} - 99q^{75} + 88q^{76} - 176q^{77} + 99q^{78} - 44q^{79} + 198q^{80} - 198q^{81} + 110q^{82} - 44q^{83} + 143q^{84} - 352q^{85} + 220q^{86} - 66q^{87} + 154q^{88} - 132q^{89} + 220q^{90} - 88q^{91} + 198q^{92} - 308q^{93} + 132q^{94} - 66q^{95} + 198q^{96} - 110q^{97} + 176q^{98} - 44q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$

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
276.2.a $$\chi_{276}(1, \cdot)$$ 276.2.a.a 2 1
276.2.a.b 2
276.2.c $$\chi_{276}(47, \cdot)$$ 276.2.c.a 22 1
276.2.c.b 22
276.2.e $$\chi_{276}(91, \cdot)$$ 276.2.e.a 24 1
276.2.g $$\chi_{276}(137, \cdot)$$ 276.2.g.a 8 1
276.2.i $$\chi_{276}(13, \cdot)$$ 276.2.i.a 20 10
276.2.i.b 20
276.2.k $$\chi_{276}(5, \cdot)$$ 276.2.k.a 80 10
276.2.m $$\chi_{276}(7, \cdot)$$ 276.2.m.a 240 10
276.2.o $$\chi_{276}(35, \cdot)$$ 276.2.o.a 440 10

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(276))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(276)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 2}$$