# Properties

 Label 3328.1 Level 3328 Weight 1 Dimension 112 Nonzero newspaces 13 Newform subspaces 33 Sturm bound 688128 Trace bound 41

## Defining parameters

 Level: $$N$$ = $$3328 = 2^{8} \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$13$$ Newform subspaces: $$33$$ Sturm bound: $$688128$$ Trace bound: $$41$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3328))$$.

Total New Old
Modular forms 4568 1256 3312
Cusp forms 344 112 232
Eisenstein series 4224 1144 3080

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 56 8 48 0

## Trace form

 $$112 q + O(q^{10})$$ $$112 q - 24 q^{17} + 20 q^{25} - 4 q^{33} + 8 q^{41} + 4 q^{49} + 24 q^{57} - 24 q^{65} + 8 q^{73} + 32 q^{81} - 4 q^{89} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3328))$$

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
3328.1.c $$\chi_{3328}(3327, \cdot)$$ 3328.1.c.a 2 1
3328.1.c.b 2
3328.1.c.c 2
3328.1.c.d 2
3328.1.c.e 2
3328.1.c.f 4
3328.1.d $$\chi_{3328}(1535, \cdot)$$ None 0 1
3328.1.g $$\chi_{3328}(3199, \cdot)$$ None 0 1
3328.1.h $$\chi_{3328}(1663, \cdot)$$ 3328.1.h.a 2 1
3328.1.j $$\chi_{3328}(385, \cdot)$$ 3328.1.j.a 2 2
3328.1.j.b 2
3328.1.m $$\chi_{3328}(577, \cdot)$$ 3328.1.m.a 4 2
3328.1.m.b 4
3328.1.o $$\chi_{3328}(831, \cdot)$$ 3328.1.o.a 4 2
3328.1.o.b 4
3328.1.o.c 4
3328.1.o.d 4
3328.1.q $$\chi_{3328}(703, \cdot)$$ None 0 2
3328.1.r $$\chi_{3328}(2241, \cdot)$$ 3328.1.r.a 4 2
3328.1.r.b 4
3328.1.t $$\chi_{3328}(2049, \cdot)$$ 3328.1.t.a 2 2
3328.1.t.b 2
3328.1.t.c 4
3328.1.t.d 4
3328.1.v $$\chi_{3328}(1407, \cdot)$$ 3328.1.v.a 4 2
3328.1.v.b 4
3328.1.v.c 4
3328.1.x $$\chi_{3328}(127, \cdot)$$ 3328.1.x.a 4 2
3328.1.y $$\chi_{3328}(511, \cdot)$$ 3328.1.y.a 4 2
3328.1.bb $$\chi_{3328}(1023, \cdot)$$ 3328.1.bb.a 4 2
3328.1.bb.b 4
3328.1.bb.c 4
3328.1.bc $$\chi_{3328}(801, \cdot)$$ None 0 4
3328.1.be $$\chi_{3328}(415, \cdot)$$ None 0 4
3328.1.bh $$\chi_{3328}(287, \cdot)$$ None 0 4
3328.1.bj $$\chi_{3328}(161, \cdot)$$ None 0 4
3328.1.bl $$\chi_{3328}(513, \cdot)$$ 3328.1.bl.a 4 4
3328.1.bl.b 4
3328.1.bm $$\chi_{3328}(193, \cdot)$$ None 0 4
3328.1.bo $$\chi_{3328}(191, \cdot)$$ None 0 4
3328.1.bq $$\chi_{3328}(959, \cdot)$$ None 0 4
3328.1.bt $$\chi_{3328}(1857, \cdot)$$ None 0 4
3328.1.bv $$\chi_{3328}(2177, \cdot)$$ 3328.1.bv.a 4 4
3328.1.bv.b 4
3328.1.bx $$\chi_{3328}(177, \cdot)$$ None 0 8
3328.1.bz $$\chi_{3328}(207, \cdot)$$ None 0 8
3328.1.ca $$\chi_{3328}(79, \cdot)$$ None 0 8
3328.1.cd $$\chi_{3328}(369, \cdot)$$ None 0 8
3328.1.ce $$\chi_{3328}(609, \cdot)$$ None 0 8
3328.1.cg $$\chi_{3328}(159, \cdot)$$ None 0 8
3328.1.cj $$\chi_{3328}(95, \cdot)$$ None 0 8
3328.1.cl $$\chi_{3328}(33, \cdot)$$ None 0 8
3328.1.cm $$\chi_{3328}(265, \cdot)$$ None 0 16
3328.1.co $$\chi_{3328}(103, \cdot)$$ None 0 16
3328.1.cq $$\chi_{3328}(183, \cdot)$$ None 0 16
3328.1.ct $$\chi_{3328}(57, \cdot)$$ None 0 16
3328.1.cu $$\chi_{3328}(305, \cdot)$$ None 0 16
3328.1.cw $$\chi_{3328}(303, \cdot)$$ None 0 16
3328.1.cz $$\chi_{3328}(367, \cdot)$$ None 0 16
3328.1.da $$\chi_{3328}(145, \cdot)$$ None 0 16
3328.1.dd $$\chi_{3328}(5, \cdot)$$ None 0 32
3328.1.dg $$\chi_{3328}(27, \cdot)$$ None 0 32
3328.1.dh $$\chi_{3328}(51, \cdot)$$ None 0 32
3328.1.dj $$\chi_{3328}(21, \cdot)$$ None 0 32
3328.1.dl $$\chi_{3328}(41, \cdot)$$ None 0 32
3328.1.dn $$\chi_{3328}(55, \cdot)$$ None 0 32
3328.1.dp $$\chi_{3328}(23, \cdot)$$ None 0 32
3328.1.dq $$\chi_{3328}(137, \cdot)$$ None 0 32
3328.1.ds $$\chi_{3328}(37, \cdot)$$ None 0 64
3328.1.du $$\chi_{3328}(3, \cdot)$$ None 0 64
3328.1.dv $$\chi_{3328}(43, \cdot)$$ None 0 64
3328.1.dy $$\chi_{3328}(141, \cdot)$$ None 0 64

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3328))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3328)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 7}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(832))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1664))$$$$^{\oplus 2}$$