## Defining parameters

 Level: $$N$$ = $$1441 = 11 \cdot 131$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$171600$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1441))$$.

Total New Old
Modular forms 1324 1180 144
Cusp forms 24 20 4
Eisenstein series 1300 1160 140

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

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

## Trace form

 $$20q - 5q^{4} - 5q^{9} + O(q^{10})$$ $$20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1441))$$

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
1441.1.b $$\chi_{1441}(263, \cdot)$$ None 0 1
1441.1.c $$\chi_{1441}(1178, \cdot)$$ None 0 1
1441.1.k $$\chi_{1441}(697, \cdot)$$ None 0 4
1441.1.l $$\chi_{1441}(61, \cdot)$$ None 0 4
1441.1.r $$\chi_{1441}(201, \cdot)$$ None 0 4
1441.1.s $$\chi_{1441}(875, \cdot)$$ None 0 4
1441.1.t $$\chi_{1441}(446, \cdot)$$ None 0 4
1441.1.u $$\chi_{1441}(130, \cdot)$$ 1441.1.u.a 20 4
1441.1.v $$\chi_{1441}(78, \cdot)$$ None 0 4
1441.1.w $$\chi_{1441}(525, \cdot)$$ None 0 4
1441.1.x $$\chi_{1441}(351, \cdot)$$ None 0 4
1441.1.y $$\chi_{1441}(42, \cdot)$$ None 0 4
1441.1.z $$\chi_{1441}(335, \cdot)$$ None 0 4
1441.1.ba $$\chi_{1441}(315, \cdot)$$ None 0 4
1441.1.be $$\chi_{1441}(155, \cdot)$$ None 0 12
1441.1.bf $$\chi_{1441}(230, \cdot)$$ None 0 12
1441.1.bn $$\chi_{1441}(7, \cdot)$$ None 0 48
1441.1.bo $$\chi_{1441}(37, \cdot)$$ None 0 48
1441.1.bp $$\chi_{1441}(14, \cdot)$$ None 0 48
1441.1.bq $$\chi_{1441}(21, \cdot)$$ None 0 48
1441.1.br $$\chi_{1441}(39, \cdot)$$ None 0 48
1441.1.bs $$\chi_{1441}(23, \cdot)$$ None 0 48
1441.1.bt $$\chi_{1441}(47, \cdot)$$ None 0 48
1441.1.bu $$\chi_{1441}(46, \cdot)$$ None 0 48
1441.1.bv $$\chi_{1441}(105, \cdot)$$ None 0 48
1441.1.bw $$\chi_{1441}(115, \cdot)$$ None 0 48
1441.1.cc $$\chi_{1441}(28, \cdot)$$ None 0 48
1441.1.cd $$\chi_{1441}(26, \cdot)$$ None 0 48

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1441))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1441)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(131))$$$$^{\oplus 2}$$