## Defining parameters

 Level: $$N$$ = $$608 = 2^{5} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$41$$ Sturm bound: $$46080$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(608))$$.

Total New Old
Modular forms 12096 6614 5482
Cusp forms 10945 6274 4671
Eisenstein series 1151 340 811

## Trace form

 $$6274 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 60 q^{5} - 64 q^{6} - 46 q^{7} - 64 q^{8} - 94 q^{9} + O(q^{10})$$ $$6274 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 60 q^{5} - 64 q^{6} - 46 q^{7} - 64 q^{8} - 94 q^{9} - 80 q^{10} - 46 q^{11} - 96 q^{12} - 76 q^{13} - 96 q^{14} - 54 q^{15} - 104 q^{16} - 40 q^{17} - 104 q^{18} - 50 q^{19} - 168 q^{20} - 64 q^{21} - 88 q^{22} - 62 q^{23} - 40 q^{24} - 98 q^{25} - 24 q^{26} - 94 q^{27} - 24 q^{28} - 44 q^{29} - 86 q^{31} - 24 q^{32} - 164 q^{33} - 40 q^{34} - 94 q^{35} - 8 q^{36} - 60 q^{37} - 76 q^{38} - 148 q^{39} - 88 q^{40} - 120 q^{41} - 104 q^{42} - 62 q^{43} - 144 q^{44} - 100 q^{45} - 128 q^{46} - 54 q^{47} - 168 q^{48} - 22 q^{49} - 144 q^{50} - 38 q^{51} - 80 q^{52} - 124 q^{53} - 88 q^{54} + 18 q^{55} - 88 q^{56} - 104 q^{57} - 128 q^{58} + 18 q^{59} - 56 q^{60} - 108 q^{61} - 24 q^{62} + 42 q^{63} + 8 q^{64} - 140 q^{65} - 16 q^{66} + 34 q^{67} - 104 q^{68} - 128 q^{69} - 40 q^{70} + 18 q^{71} - 112 q^{72} - 88 q^{73} - 96 q^{74} - 40 q^{75} - 68 q^{76} - 168 q^{77} - 144 q^{78} - 54 q^{79} - 56 q^{80} - 54 q^{81} - 64 q^{82} - 126 q^{83} - 104 q^{84} - 96 q^{85} - 24 q^{86} - 158 q^{87} - 72 q^{88} - 120 q^{89} - 88 q^{90} - 142 q^{91} + 8 q^{92} - 40 q^{93} - 88 q^{94} - 110 q^{95} - 144 q^{96} - 200 q^{97} - 24 q^{98} - 150 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$

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
608.2.a $$\chi_{608}(1, \cdot)$$ 608.2.a.a 1 1
608.2.a.b 1
608.2.a.c 1
608.2.a.d 1
608.2.a.e 1
608.2.a.f 1
608.2.a.g 2
608.2.a.h 2
608.2.a.i 4
608.2.a.j 4
608.2.b $$\chi_{608}(303, \cdot)$$ 608.2.b.a 2 1
608.2.b.b 4
608.2.b.c 12
608.2.c $$\chi_{608}(305, \cdot)$$ 608.2.c.a 2 1
608.2.c.b 16
608.2.h $$\chi_{608}(607, \cdot)$$ 608.2.h.a 20 1
608.2.i $$\chi_{608}(353, \cdot)$$ 608.2.i.a 2 2
608.2.i.b 2
608.2.i.c 8
608.2.i.d 8
608.2.i.e 8
608.2.i.f 12
608.2.k $$\chi_{608}(153, \cdot)$$ None 0 2
608.2.m $$\chi_{608}(151, \cdot)$$ None 0 2
608.2.n $$\chi_{608}(31, \cdot)$$ 608.2.n.a 40 2
608.2.s $$\chi_{608}(335, \cdot)$$ 608.2.s.a 4 2
608.2.s.b 4
608.2.s.c 28
608.2.t $$\chi_{608}(49, \cdot)$$ 608.2.t.a 36 2
608.2.u $$\chi_{608}(75, \cdot)$$ 608.2.u.a 312 4
608.2.v $$\chi_{608}(77, \cdot)$$ 608.2.v.a 288 4
608.2.y $$\chi_{608}(161, \cdot)$$ 608.2.y.a 24 6
608.2.y.b 30
608.2.y.c 30
608.2.y.d 36
608.2.z $$\chi_{608}(121, \cdot)$$ None 0 4
608.2.bb $$\chi_{608}(103, \cdot)$$ None 0 4
608.2.bf $$\chi_{608}(17, \cdot)$$ 608.2.bf.a 108 6
608.2.bh $$\chi_{608}(15, \cdot)$$ 608.2.bh.a 12 6
608.2.bh.b 96
608.2.bi $$\chi_{608}(127, \cdot)$$ 608.2.bi.a 120 6
608.2.bm $$\chi_{608}(45, \cdot)$$ 608.2.bm.a 624 8
608.2.bn $$\chi_{608}(27, \cdot)$$ 608.2.bn.a 624 8
608.2.bo $$\chi_{608}(71, \cdot)$$ None 0 12
608.2.bq $$\chi_{608}(9, \cdot)$$ None 0 12
608.2.bs $$\chi_{608}(5, \cdot)$$ 608.2.bs.a 1872 24
608.2.bt $$\chi_{608}(3, \cdot)$$ 608.2.bt.a 1872 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(608))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(608)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$