## Defining parameters

 Level: $$N$$ = $$3267 = 3^{3} \cdot 11^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$11$$ Newform subspaces: $$20$$ Sturm bound: $$784080$$ Trace bound: $$20$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3267))$$.

Total New Old
Modular forms 5087 2400 2687
Cusp forms 287 152 135
Eisenstein series 4800 2248 2552

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 112 0 40 0

## Trace form

 $$152 q + q^{4} + 4 q^{5} + O(q^{10})$$ $$152 q + q^{4} + 4 q^{5} + 3 q^{15} + q^{16} - 5 q^{20} + 8 q^{23} + 3 q^{25} + 3 q^{27} + 2 q^{31} - 40 q^{34} - 6 q^{36} + 2 q^{37} + 4 q^{47} + 3 q^{48} + q^{49} - 2 q^{53} + 4 q^{59} + q^{64} - 17 q^{67} - 2 q^{71} - 6 q^{75} - 2 q^{80} - 49 q^{89} - 2 q^{92} - 6 q^{93} - 7 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3267))$$

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
3267.1.b $$\chi_{3267}(485, \cdot)$$ 3267.1.b.a 1 1
3267.1.b.b 1
3267.1.b.c 2
3267.1.b.d 2
3267.1.b.e 2
3267.1.c $$\chi_{3267}(2782, \cdot)$$ 3267.1.c.a 4 1
3267.1.h $$\chi_{3267}(604, \cdot)$$ 3267.1.h.a 4 2
3267.1.i $$\chi_{3267}(1574, \cdot)$$ 3267.1.i.a 2 2
3267.1.l $$\chi_{3267}(838, \cdot)$$ 3267.1.l.a 16 4
3267.1.m $$\chi_{3267}(269, \cdot)$$ 3267.1.m.a 4 4
3267.1.m.b 4
3267.1.m.c 8
3267.1.m.d 8
3267.1.m.e 8
3267.1.q $$\chi_{3267}(122, \cdot)$$ 3267.1.q.a 6 6
3267.1.r $$\chi_{3267}(241, \cdot)$$ None 0 6
3267.1.t $$\chi_{3267}(109, \cdot)$$ None 0 10
3267.1.u $$\chi_{3267}(188, \cdot)$$ None 0 10
3267.1.v $$\chi_{3267}(251, \cdot)$$ 3267.1.v.a 8 8
3267.1.w $$\chi_{3267}(118, \cdot)$$ 3267.1.w.a 8 8
3267.1.w.b 16
3267.1.bb $$\chi_{3267}(89, \cdot)$$ None 0 20
3267.1.bc $$\chi_{3267}(10, \cdot)$$ None 0 20
3267.1.be $$\chi_{3267}(245, \cdot)$$ 3267.1.be.a 24 24
3267.1.bf $$\chi_{3267}(40, \cdot)$$ 3267.1.bf.a 24 24
3267.1.bi $$\chi_{3267}(26, \cdot)$$ None 0 40
3267.1.bj $$\chi_{3267}(28, \cdot)$$ None 0 40
3267.1.bm $$\chi_{3267}(43, \cdot)$$ None 0 60
3267.1.bn $$\chi_{3267}(23, \cdot)$$ None 0 60
3267.1.bq $$\chi_{3267}(19, \cdot)$$ None 0 80
3267.1.br $$\chi_{3267}(71, \cdot)$$ None 0 80
3267.1.bu $$\chi_{3267}(7, \cdot)$$ None 0 240
3267.1.bv $$\chi_{3267}(5, \cdot)$$ None 0 240

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3267))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3267)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(297))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1089))$$$$^{\oplus 2}$$