## Defining parameters

 Level: $$N$$ = $$592 = 2^{4} \cdot 37$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$7$$ Sturm bound: $$21888$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(592))$$.

Total New Old
Modular forms 565 177 388
Cusp forms 61 19 42
Eisenstein series 504 158 346

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 11 0 8 0

## Trace form

 $$19 q - 4 q^{5} + 4 q^{7} - 2 q^{9} + O(q^{10})$$ $$19 q - 4 q^{5} + 4 q^{7} - 2 q^{9} + 2 q^{13} + 2 q^{15} - 2 q^{19} - 6 q^{21} + 2 q^{25} - 4 q^{29} + 10 q^{33} - 2 q^{35} - 2 q^{37} - 2 q^{39} - 2 q^{43} - 4 q^{45} - 6 q^{49} - 2 q^{51} + 2 q^{53} + 2 q^{55} - 6 q^{57} - 7 q^{61} - 9 q^{65} - 4 q^{71} + 2 q^{73} - 4 q^{75} + 6 q^{77} + 2 q^{79} + 4 q^{83} - 13 q^{85} + 4 q^{87} - 9 q^{89} + 2 q^{91} + 4 q^{93} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(592))$$

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
592.1.b $$\chi_{592}(591, \cdot)$$ 592.1.b.a 1 1
592.1.b.b 2
592.1.d $$\chi_{592}(223, \cdot)$$ None 0 1
592.1.f $$\chi_{592}(519, \cdot)$$ None 0 1
592.1.h $$\chi_{592}(295, \cdot)$$ None 0 1
592.1.k $$\chi_{592}(401, \cdot)$$ 592.1.k.a 2 2
592.1.k.b 2
592.1.l $$\chi_{592}(117, \cdot)$$ None 0 2
592.1.p $$\chi_{592}(75, \cdot)$$ None 0 2
592.1.q $$\chi_{592}(147, \cdot)$$ None 0 2
592.1.r $$\chi_{592}(413, \cdot)$$ None 0 2
592.1.u $$\chi_{592}(105, \cdot)$$ None 0 2
592.1.v $$\chi_{592}(455, \cdot)$$ None 0 2
592.1.x $$\chi_{592}(343, \cdot)$$ None 0 2
592.1.z $$\chi_{592}(47, \cdot)$$ 592.1.z.a 4 2
592.1.bb $$\chi_{592}(159, \cdot)$$ 592.1.bb.a 2 2
592.1.bd $$\chi_{592}(393, \cdot)$$ None 0 4
592.1.bg $$\chi_{592}(45, \cdot)$$ None 0 4
592.1.bh $$\chi_{592}(11, \cdot)$$ None 0 4
592.1.bi $$\chi_{592}(195, \cdot)$$ None 0 4
592.1.bm $$\chi_{592}(29, \cdot)$$ None 0 4
592.1.bn $$\chi_{592}(97, \cdot)$$ None 0 4
592.1.bp $$\chi_{592}(151, \cdot)$$ None 0 6
592.1.br $$\chi_{592}(7, \cdot)$$ None 0 6
592.1.bt $$\chi_{592}(95, \cdot)$$ 592.1.bt.a 6 6
592.1.bu $$\chi_{592}(127, \cdot)$$ None 0 6
592.1.bw $$\chi_{592}(57, \cdot)$$ None 0 12
592.1.bz $$\chi_{592}(83, \cdot)$$ None 0 12
592.1.cb $$\chi_{592}(13, \cdot)$$ None 0 12
592.1.cc $$\chi_{592}(5, \cdot)$$ None 0 12
592.1.cf $$\chi_{592}(3, \cdot)$$ None 0 12
592.1.cg $$\chi_{592}(17, \cdot)$$ None 0 12

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(592))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(592)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(296))$$$$^{\oplus 2}$$