## Defining parameters

 Level: $$N$$ = $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$10$$ Sturm bound: $$5376$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(273))$$.

Total New Old
Modular forms 318 140 178
Cusp forms 30 28 2
Eisenstein series 288 112 176

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 20 8 0 0

## Trace form

 $$28 q - 4 q^{6} - 6 q^{9} + O(q^{10})$$ $$28 q - 4 q^{6} - 6 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} - 4 q^{15} - 6 q^{16} - 4 q^{19} - 2 q^{21} + 2 q^{24} - 2 q^{28} + 8 q^{34} - 2 q^{37} - 4 q^{39} + 4 q^{40} + 2 q^{42} - 12 q^{43} + 2 q^{46} - 2 q^{49} + 4 q^{51} - 4 q^{52} - 2 q^{54} - 4 q^{57} + 2 q^{58} - 4 q^{63} - 8 q^{64} - 4 q^{67} + 4 q^{69} - 8 q^{70} + 4 q^{73} + 8 q^{75} + 8 q^{76} + 4 q^{78} - 4 q^{79} + 10 q^{81} - 2 q^{82} + 10 q^{84} - 4 q^{85} - 2 q^{87} + 8 q^{90} + 8 q^{91} + 8 q^{93} - 2 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(273))$$

We only show spaces with odd 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
273.1.b $$\chi_{273}(92, \cdot)$$ None 0 1
273.1.d $$\chi_{273}(181, \cdot)$$ None 0 1
273.1.f $$\chi_{273}(118, \cdot)$$ None 0 1
273.1.h $$\chi_{273}(155, \cdot)$$ None 0 1
273.1.m $$\chi_{273}(148, \cdot)$$ None 0 2
273.1.o $$\chi_{273}(83, \cdot)$$ 273.1.o.a 2 2
273.1.o.b 2
273.1.q $$\chi_{273}(166, \cdot)$$ None 0 2
273.1.s $$\chi_{273}(74, \cdot)$$ 273.1.s.a 2 2
273.1.s.b 4
273.1.v $$\chi_{273}(55, \cdot)$$ None 0 2
273.1.w $$\chi_{273}(116, \cdot)$$ None 0 2
273.1.x $$\chi_{273}(179, \cdot)$$ 273.1.x.a 2 2
273.1.z $$\chi_{273}(61, \cdot)$$ None 0 2
273.1.bb $$\chi_{273}(40, \cdot)$$ None 0 2
273.1.bc $$\chi_{273}(134, \cdot)$$ None 0 2
273.1.be $$\chi_{273}(29, \cdot)$$ None 0 2
273.1.bg $$\chi_{273}(10, \cdot)$$ None 0 2
273.1.bi $$\chi_{273}(103, \cdot)$$ None 0 2
273.1.bk $$\chi_{273}(53, \cdot)$$ None 0 2
273.1.bm $$\chi_{273}(191, \cdot)$$ 273.1.bm.a 2 2
273.1.bm.b 4
273.1.bo $$\chi_{273}(160, \cdot)$$ None 0 2
273.1.bp $$\chi_{273}(23, \cdot)$$ 273.1.bp.a 2 2
273.1.bq $$\chi_{273}(178, \cdot)$$ None 0 2
273.1.bs $$\chi_{273}(59, \cdot)$$ 273.1.bs.a 4 4
273.1.bu $$\chi_{273}(37, \cdot)$$ None 0 4
273.1.bx $$\chi_{273}(58, \cdot)$$ None 0 4
273.1.ca $$\chi_{273}(20, \cdot)$$ None 0 4
273.1.cb $$\chi_{273}(5, \cdot)$$ None 0 4
273.1.ce $$\chi_{273}(85, \cdot)$$ None 0 4
273.1.cf $$\chi_{273}(109, \cdot)$$ None 0 4
273.1.ch $$\chi_{273}(80, \cdot)$$ 273.1.ch.a 4 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(273))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(273)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 2}$$