# Properties

 Label 368.2 Level 368 Weight 2 Dimension 2273 Nonzero newspaces 8 Newform subspaces 28 Sturm bound 16896 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$368 = 2^{4} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$28$$ Sturm bound: $$16896$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(368))$$.

Total New Old
Modular forms 4532 2461 2071
Cusp forms 3917 2273 1644
Eisenstein series 615 188 427

## Trace form

 $$2273q - 40q^{2} - 29q^{3} - 44q^{4} - 51q^{5} - 52q^{6} - 33q^{7} - 52q^{8} - 11q^{9} + O(q^{10})$$ $$2273q - 40q^{2} - 29q^{3} - 44q^{4} - 51q^{5} - 52q^{6} - 33q^{7} - 52q^{8} - 11q^{9} - 44q^{10} - 37q^{11} - 36q^{12} - 51q^{13} - 36q^{14} - 41q^{15} - 28q^{16} - 91q^{17} - 48q^{18} - 45q^{19} - 52q^{20} - 63q^{21} - 44q^{22} - 33q^{23} - 88q^{24} - 11q^{25} - 52q^{26} - 17q^{27} - 60q^{28} - 67q^{29} - 36q^{30} - q^{31} - 60q^{32} - 91q^{33} - 52q^{34} - 25q^{35} - 36q^{36} - 67q^{37} - 20q^{38} - 33q^{39} - 28q^{40} - 11q^{41} - 44q^{42} - 53q^{43} - 36q^{44} - 70q^{45} - 56q^{46} - 98q^{47} - 60q^{48} - 111q^{49} - 32q^{50} - 41q^{51} - 36q^{52} - 35q^{53} - 44q^{54} - 33q^{55} - 28q^{56} - 11q^{57} - 20q^{58} - 21q^{59} - 44q^{60} - 19q^{61} - 76q^{62} - 41q^{63} - 44q^{64} - 107q^{65} - 52q^{66} - 13q^{67} - 44q^{68} - 43q^{69} - 104q^{70} - 33q^{71} - 52q^{72} - 11q^{73} - 44q^{74} - 111q^{75} - 68q^{76} - 107q^{77} - 36q^{78} - 99q^{79} - 60q^{80} - 295q^{81} - 44q^{82} - 95q^{83} - 28q^{84} - 195q^{85} - 44q^{86} - 231q^{87} - 60q^{88} - 99q^{89} - 36q^{90} - 162q^{91} - 20q^{92} - 274q^{93} - 12q^{94} - 141q^{95} - 12q^{96} - 179q^{97} - 32q^{98} - 227q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$

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
368.2.a $$\chi_{368}(1, \cdot)$$ 368.2.a.a 1 1
368.2.a.b 1
368.2.a.c 1
368.2.a.d 1
368.2.a.e 1
368.2.a.f 1
368.2.a.g 1
368.2.a.h 2
368.2.a.i 2
368.2.b $$\chi_{368}(185, \cdot)$$ None 0 1
368.2.c $$\chi_{368}(367, \cdot)$$ 368.2.c.a 4 1
368.2.c.b 8
368.2.h $$\chi_{368}(183, \cdot)$$ None 0 1
368.2.i $$\chi_{368}(91, \cdot)$$ 368.2.i.a 12 2
368.2.i.b 80
368.2.j $$\chi_{368}(93, \cdot)$$ 368.2.j.a 2 2
368.2.j.b 4
368.2.j.c 12
368.2.j.d 24
368.2.j.e 46
368.2.m $$\chi_{368}(49, \cdot)$$ 368.2.m.a 10 10
368.2.m.b 10
368.2.m.c 10
368.2.m.d 20
368.2.m.e 30
368.2.m.f 30
368.2.n $$\chi_{368}(7, \cdot)$$ None 0 10
368.2.s $$\chi_{368}(15, \cdot)$$ 368.2.s.a 40 10
368.2.s.b 80
368.2.t $$\chi_{368}(9, \cdot)$$ None 0 10
368.2.w $$\chi_{368}(13, \cdot)$$ 368.2.w.a 920 20
368.2.x $$\chi_{368}(11, \cdot)$$ 368.2.x.a 920 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(368))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(368)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 2}$$