# Properties

 Label 230.4 Level 230 Weight 4 Dimension 1446 Nonzero newspaces 6 Newform subspaces 19 Sturm bound 12672 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$19$$ Sturm bound: $$12672$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(230))$$.

Total New Old
Modular forms 4928 1446 3482
Cusp forms 4576 1446 3130
Eisenstein series 352 0 352

## Trace form

 $$1446 q - 4 q^{2} + 16 q^{3} + 8 q^{4} + 10 q^{5} + 16 q^{6} + 8 q^{7} - 16 q^{8} - 166 q^{9} + O(q^{10})$$ $$1446 q - 4 q^{2} + 16 q^{3} + 8 q^{4} + 10 q^{5} + 16 q^{6} + 8 q^{7} - 16 q^{8} - 166 q^{9} - 100 q^{10} + 88 q^{11} + 64 q^{12} + 116 q^{13} + 224 q^{14} - 588 q^{15} - 96 q^{16} - 484 q^{17} + 28 q^{18} + 400 q^{19} + 232 q^{20} + 2368 q^{21} + 920 q^{22} + 1804 q^{23} + 192 q^{24} + 954 q^{25} + 576 q^{26} + 424 q^{27} - 320 q^{28} - 340 q^{29} - 1256 q^{30} - 1992 q^{31} - 64 q^{32} - 3680 q^{33} - 776 q^{34} - 2430 q^{35} + 72 q^{36} - 2308 q^{37} + 400 q^{38} - 568 q^{39} + 240 q^{40} + 1008 q^{41} - 128 q^{42} + 3368 q^{43} - 544 q^{44} + 3060 q^{45} - 32 q^{46} + 4192 q^{47} + 256 q^{48} + 6342 q^{49} + 700 q^{50} + 2888 q^{51} + 464 q^{52} - 928 q^{53} - 6728 q^{54} - 7676 q^{55} - 4640 q^{56} - 17704 q^{57} - 3336 q^{58} - 10820 q^{59} - 88 q^{60} - 1860 q^{61} + 2824 q^{62} + 8656 q^{63} + 128 q^{64} + 9684 q^{65} + 11744 q^{66} + 7856 q^{67} + 5456 q^{68} + 15784 q^{69} + 4848 q^{70} + 17288 q^{71} + 4336 q^{72} + 3500 q^{73} + 8712 q^{74} - 378 q^{75} + 1760 q^{76} - 784 q^{77} - 4760 q^{78} - 12812 q^{79} - 1248 q^{80} - 18126 q^{81} - 8280 q^{82} - 18052 q^{83} - 6992 q^{84} - 5998 q^{85} - 13496 q^{86} + 7932 q^{87} - 192 q^{88} + 160 q^{89} - 2580 q^{90} + 6296 q^{91} - 528 q^{92} + 2432 q^{93} + 2624 q^{94} + 23232 q^{95} + 256 q^{96} + 25816 q^{97} + 15212 q^{98} + 34028 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(230))$$

We only show spaces with even 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
230.4.a $$\chi_{230}(1, \cdot)$$ 230.4.a.a 1 1
230.4.a.b 1
230.4.a.c 1
230.4.a.d 1
230.4.a.e 1
230.4.a.f 2
230.4.a.g 3
230.4.a.h 4
230.4.a.i 4
230.4.a.j 4
230.4.b $$\chi_{230}(139, \cdot)$$ 230.4.b.a 14 1
230.4.b.b 18
230.4.e $$\chi_{230}(137, \cdot)$$ 230.4.e.a 72 2
230.4.g $$\chi_{230}(31, \cdot)$$ 230.4.g.a 50 10
230.4.g.b 60
230.4.g.c 60
230.4.g.d 70
230.4.j $$\chi_{230}(9, \cdot)$$ 230.4.j.a 360 10
230.4.l $$\chi_{230}(7, \cdot)$$ 230.4.l.a 720 20

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(230))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(230)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 2}$$