## Defining parameters

 Level: $$N$$ = $$154 = 2 \cdot 7 \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$8$$ Newform subspaces: $$25$$ Sturm bound: $$5760$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(154))$$.

Total New Old
Modular forms 2280 678 1602
Cusp forms 2040 678 1362
Eisenstein series 240 0 240

## Trace form

 $$678 q - 24 q^{3} + 48 q^{5} - 28 q^{6} + 76 q^{7} + 236 q^{9} + O(q^{10})$$ $$678 q - 24 q^{3} + 48 q^{5} - 28 q^{6} + 76 q^{7} + 236 q^{9} + 128 q^{10} + 158 q^{11} + 64 q^{12} - 52 q^{13} - 284 q^{14} - 796 q^{15} - 320 q^{17} - 124 q^{18} + 570 q^{19} + 240 q^{20} + 564 q^{21} + 216 q^{22} - 192 q^{23} - 304 q^{24} - 1020 q^{25} - 1096 q^{26} - 1302 q^{27} - 120 q^{28} - 652 q^{29} + 1224 q^{30} - 600 q^{31} + 320 q^{32} + 3100 q^{33} + 2016 q^{34} + 1850 q^{35} + 536 q^{36} + 396 q^{37} - 96 q^{38} + 824 q^{39} - 768 q^{40} - 76 q^{41} - 2828 q^{42} - 4348 q^{43} - 2288 q^{44} - 3664 q^{45} - 384 q^{46} + 536 q^{47} + 192 q^{48} + 1510 q^{49} + 1312 q^{50} - 878 q^{51} + 1296 q^{52} - 3124 q^{53} + 4608 q^{54} - 592 q^{55} - 96 q^{56} + 1266 q^{57} + 4368 q^{58} + 4178 q^{59} + 1968 q^{60} + 7640 q^{61} + 5040 q^{62} + 17456 q^{63} - 768 q^{64} + 12592 q^{65} + 2704 q^{66} + 4156 q^{67} - 1520 q^{68} - 3336 q^{69} - 5448 q^{70} - 2976 q^{71} - 3136 q^{72} - 8592 q^{73} - 8624 q^{74} - 25898 q^{75} - 5968 q^{76} - 16536 q^{77} - 14144 q^{78} - 15180 q^{79} - 1792 q^{80} - 32058 q^{81} - 6932 q^{82} - 14998 q^{83} - 2416 q^{84} - 6280 q^{85} - 4060 q^{86} - 1208 q^{87} + 896 q^{88} + 4280 q^{89} + 14784 q^{90} + 18478 q^{91} + 4224 q^{92} + 22232 q^{93} + 18632 q^{94} + 24476 q^{95} + 384 q^{96} + 15138 q^{97} + 6260 q^{98} + 19312 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(154))$$

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
154.4.a $$\chi_{154}(1, \cdot)$$ 154.4.a.a 1 1
154.4.a.b 1
154.4.a.c 1
154.4.a.d 1
154.4.a.e 1
154.4.a.f 2
154.4.a.g 2
154.4.a.h 2
154.4.a.i 3
154.4.c $$\chi_{154}(153, \cdot)$$ 154.4.c.a 24 1
154.4.e $$\chi_{154}(23, \cdot)$$ 154.4.e.a 10 2
154.4.e.b 10
154.4.e.c 10
154.4.e.d 10
154.4.f $$\chi_{154}(15, \cdot)$$ 154.4.f.a 4 4
154.4.f.b 4
154.4.f.c 8
154.4.f.d 16
154.4.f.e 20
154.4.f.f 20
154.4.i $$\chi_{154}(87, \cdot)$$ 154.4.i.a 48 2
154.4.k $$\chi_{154}(13, \cdot)$$ 154.4.k.a 96 4
154.4.m $$\chi_{154}(9, \cdot)$$ 154.4.m.a 96 8
154.4.m.b 96
154.4.n $$\chi_{154}(17, \cdot)$$ 154.4.n.a 192 8

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(154))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(154)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 2}$$