## Defining parameters

 Level: $$N$$ = $$2888 = 2^{3} \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Sturm bound: $$1039680$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2888))$$.

Total New Old
Modular forms 262944 146333 116611
Cusp forms 256897 144459 112438
Eisenstein series 6047 1874 4173

## Trace form

 $$144459 q - 306 q^{2} - 306 q^{3} - 306 q^{4} - 306 q^{6} - 306 q^{7} - 306 q^{8} - 612 q^{9} + O(q^{10})$$ $$144459 q - 306 q^{2} - 306 q^{3} - 306 q^{4} - 306 q^{6} - 306 q^{7} - 306 q^{8} - 612 q^{9} - 306 q^{10} - 306 q^{11} - 306 q^{12} - 306 q^{14} - 306 q^{15} - 306 q^{16} - 612 q^{17} - 306 q^{18} - 324 q^{19} - 594 q^{20} - 306 q^{22} - 306 q^{23} - 306 q^{24} - 612 q^{25} - 306 q^{26} - 288 q^{27} - 306 q^{28} + 36 q^{29} - 306 q^{30} - 270 q^{31} - 306 q^{32} - 504 q^{33} - 306 q^{34} - 234 q^{35} - 306 q^{36} + 36 q^{37} - 324 q^{38} - 486 q^{39} - 306 q^{40} - 576 q^{41} - 306 q^{42} - 234 q^{43} - 306 q^{44} + 108 q^{45} - 306 q^{46} - 270 q^{47} - 306 q^{48} - 576 q^{49} - 306 q^{50} - 288 q^{51} - 306 q^{52} - 414 q^{54} - 306 q^{55} - 306 q^{56} - 648 q^{57} - 594 q^{58} - 306 q^{59} - 378 q^{60} - 36 q^{61} - 486 q^{62} - 450 q^{63} - 594 q^{64} - 720 q^{65} - 594 q^{66} - 522 q^{67} - 558 q^{68} - 738 q^{70} - 414 q^{71} - 846 q^{72} - 774 q^{73} - 594 q^{74} - 594 q^{75} - 504 q^{76} - 108 q^{77} - 666 q^{78} - 558 q^{79} - 594 q^{80} - 774 q^{81} - 846 q^{82} - 414 q^{83} - 738 q^{84} - 558 q^{86} - 522 q^{87} - 594 q^{88} - 720 q^{89} - 594 q^{90} - 450 q^{91} - 486 q^{92} - 36 q^{93} - 378 q^{94} - 288 q^{95} - 594 q^{96} - 540 q^{97} - 306 q^{98} - 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2888))$$

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
2888.2.a $$\chi_{2888}(1, \cdot)$$ 2888.2.a.a 1 1
2888.2.a.b 1
2888.2.a.c 1
2888.2.a.d 1
2888.2.a.e 1
2888.2.a.f 1
2888.2.a.g 2
2888.2.a.h 2
2888.2.a.i 2
2888.2.a.j 2
2888.2.a.k 2
2888.2.a.l 2
2888.2.a.m 3
2888.2.a.n 3
2888.2.a.o 3
2888.2.a.p 3
2888.2.a.q 3
2888.2.a.r 3
2888.2.a.s 3
2888.2.a.t 6
2888.2.a.u 6
2888.2.a.v 8
2888.2.a.w 8
2888.2.a.x 9
2888.2.a.y 9
2888.2.b $$\chi_{2888}(1443, \cdot)$$ n/a 324 1
2888.2.c $$\chi_{2888}(1445, \cdot)$$ n/a 324 1
2888.2.h $$\chi_{2888}(2887, \cdot)$$ None 0 1
2888.2.i $$\chi_{2888}(1873, \cdot)$$ n/a 170 2
2888.2.j $$\chi_{2888}(791, \cdot)$$ None 0 2
2888.2.o $$\chi_{2888}(2235, \cdot)$$ n/a 648 2
2888.2.p $$\chi_{2888}(429, \cdot)$$ n/a 648 2
2888.2.q $$\chi_{2888}(1137, \cdot)$$ n/a 510 6
2888.2.t $$\chi_{2888}(245, \cdot)$$ n/a 1944 6
2888.2.v $$\chi_{2888}(299, \cdot)$$ n/a 1944 6
2888.2.w $$\chi_{2888}(127, \cdot)$$ None 0 6
2888.2.y $$\chi_{2888}(153, \cdot)$$ n/a 1710 18
2888.2.z $$\chi_{2888}(151, \cdot)$$ None 0 18
2888.2.be $$\chi_{2888}(77, \cdot)$$ n/a 6804 18
2888.2.bf $$\chi_{2888}(75, \cdot)$$ n/a 6804 18
2888.2.bg $$\chi_{2888}(49, \cdot)$$ n/a 3420 36
2888.2.bh $$\chi_{2888}(45, \cdot)$$ n/a 13608 36
2888.2.bi $$\chi_{2888}(27, \cdot)$$ n/a 13608 36
2888.2.bn $$\chi_{2888}(31, \cdot)$$ None 0 36
2888.2.bo $$\chi_{2888}(9, \cdot)$$ n/a 10260 108
2888.2.bq $$\chi_{2888}(15, \cdot)$$ None 0 108
2888.2.br $$\chi_{2888}(3, \cdot)$$ n/a 40824 108
2888.2.bt $$\chi_{2888}(5, \cdot)$$ n/a 40824 108

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2888))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2888)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(722))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1444))$$$$^{\oplus 2}$$