## Defining parameters

 Level: $$N$$ = $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$202752$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1840))$$.

Total New Old
Modular forms 2654 588 2066
Cusp forms 190 22 168
Eisenstein series 2464 566 1898

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 22 0 0 0

## Trace form

 $$22q + 2q^{5} + 4q^{9} + O(q^{10})$$ $$22q + 2q^{5} + 4q^{9} - 6q^{29} + 2q^{31} + 2q^{35} + 2q^{41} - 24q^{45} - 20q^{49} + 2q^{59} + 4q^{61} + 2q^{71} - 2q^{85} - 4q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1840))$$

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
1840.1.c $$\chi_{1840}(1151, \cdot)$$ None 0 1
1840.1.d $$\chi_{1840}(1241, \cdot)$$ None 0 1
1840.1.g $$\chi_{1840}(689, \cdot)$$ 1840.1.g.a 1 1
1840.1.g.b 1
1840.1.h $$\chi_{1840}(599, \cdot)$$ None 0 1
1840.1.k $$\chi_{1840}(321, \cdot)$$ None 0 1
1840.1.l $$\chi_{1840}(231, \cdot)$$ None 0 1
1840.1.o $$\chi_{1840}(1519, \cdot)$$ None 0 1
1840.1.p $$\chi_{1840}(1609, \cdot)$$ None 0 1
1840.1.q $$\chi_{1840}(93, \cdot)$$ None 0 2
1840.1.s $$\chi_{1840}(1563, \cdot)$$ None 0 2
1840.1.v $$\chi_{1840}(139, \cdot)$$ None 0 2
1840.1.w $$\chi_{1840}(229, \cdot)$$ None 0 2
1840.1.z $$\chi_{1840}(553, \cdot)$$ None 0 2
1840.1.bb $$\chi_{1840}(183, \cdot)$$ None 0 2
1840.1.bc $$\chi_{1840}(367, \cdot)$$ None 0 2
1840.1.be $$\chi_{1840}(737, \cdot)$$ None 0 2
1840.1.bh $$\chi_{1840}(781, \cdot)$$ None 0 2
1840.1.bi $$\chi_{1840}(691, \cdot)$$ None 0 2
1840.1.bl $$\chi_{1840}(643, \cdot)$$ None 0 2
1840.1.bn $$\chi_{1840}(1013, \cdot)$$ None 0 2
1840.1.bp $$\chi_{1840}(89, \cdot)$$ None 0 10
1840.1.bq $$\chi_{1840}(239, \cdot)$$ 1840.1.bq.a 20 10
1840.1.bt $$\chi_{1840}(71, \cdot)$$ None 0 10
1840.1.bu $$\chi_{1840}(241, \cdot)$$ None 0 10
1840.1.bx $$\chi_{1840}(39, \cdot)$$ None 0 10
1840.1.by $$\chi_{1840}(129, \cdot)$$ None 0 10
1840.1.cb $$\chi_{1840}(201, \cdot)$$ None 0 10
1840.1.cc $$\chi_{1840}(31, \cdot)$$ None 0 10
1840.1.ce $$\chi_{1840}(77, \cdot)$$ None 0 20
1840.1.cg $$\chi_{1840}(83, \cdot)$$ None 0 20
1840.1.ci $$\chi_{1840}(131, \cdot)$$ None 0 20
1840.1.cl $$\chi_{1840}(21, \cdot)$$ None 0 20
1840.1.cn $$\chi_{1840}(177, \cdot)$$ None 0 20
1840.1.cp $$\chi_{1840}(63, \cdot)$$ None 0 20
1840.1.cq $$\chi_{1840}(7, \cdot)$$ None 0 20
1840.1.cs $$\chi_{1840}(73, \cdot)$$ None 0 20
1840.1.cu $$\chi_{1840}(109, \cdot)$$ None 0 20
1840.1.cx $$\chi_{1840}(59, \cdot)$$ None 0 20
1840.1.cz $$\chi_{1840}(43, \cdot)$$ None 0 20
1840.1.db $$\chi_{1840}(13, \cdot)$$ None 0 20

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1840))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1840)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(368))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(920))$$$$^{\oplus 2}$$