## Defining parameters

 Level: $$N$$ = $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$8$$ Sturm bound: $$9504$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(230))$$.

Total New Old
Modular forms 3344 964 2380
Cusp forms 2992 964 2028
Eisenstein series 352 0 352

## Trace form

 $$964q + 4q^{2} + 8q^{3} - 16q^{6} - 8q^{7} - 8q^{8} + O(q^{10})$$ $$964q + 4q^{2} + 8q^{3} - 16q^{6} - 8q^{7} - 8q^{8} + 20q^{10} + 32q^{11} + 16q^{12} - 12q^{13} + 114q^{15} + 16q^{16} + 192q^{17} + 348q^{18} + 132q^{19} + 4q^{20} + 164q^{21} - 32q^{22} - 84q^{23} - 32q^{25} - 152q^{26} - 580q^{27} - 248q^{28} - 308q^{29} - 352q^{30} - 604q^{31} - 16q^{32} - 548q^{33} + 180q^{35} + 8q^{36} + 716q^{37} + 80q^{38} + 528q^{39} + 40q^{40} + 208q^{41} - 32q^{42} + 344q^{43} - 20q^{45} - 8q^{46} - 104q^{47} - 32q^{48} - 528q^{49} - 100q^{50} - 416q^{51} - 24q^{52} - 564q^{53} + 616q^{54} + 132q^{55} + 496q^{56} + 236q^{57} + 720q^{58} + 968q^{59} + 256q^{60} + 1424q^{61} + 1000q^{62} + 1108q^{63} + 522q^{65} + 480q^{66} - 160q^{67} + 56q^{68} - 220q^{69} - 96q^{70} - 548q^{71} - 360q^{72} - 252q^{73} - 1056q^{74} - 926q^{75} - 160q^{76} - 1916q^{77} - 1368q^{78} - 1408q^{79} - 264q^{80} - 1692q^{81} - 1264q^{82} - 1700q^{83} - 704q^{84} - 756q^{85} - 1128q^{86} + 848q^{87} + 64q^{88} + 88q^{89} + 20q^{90} - 48q^{91} + 8q^{92} + 416q^{93} - 1030q^{95} + 64q^{96} - 2256q^{97} - 1244q^{98} - 4356q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(230))$$

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
230.3.c $$\chi_{230}(229, \cdot)$$ 230.3.c.a 24 1
230.3.d $$\chi_{230}(91, \cdot)$$ 230.3.d.a 16 1
230.3.f $$\chi_{230}(47, \cdot)$$ 230.3.f.a 20 2
230.3.f.b 24
230.3.h $$\chi_{230}(11, \cdot)$$ 230.3.h.a 160 10
230.3.i $$\chi_{230}(19, \cdot)$$ 230.3.i.a 240 10
230.3.k $$\chi_{230}(3, \cdot)$$ 230.3.k.a 240 20
230.3.k.b 240

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(230))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(230)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 2}$$