## Defining parameters

 Level: $$N$$ = $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Sturm bound: $$519840$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1805))$$.

Total New Old
Modular forms 131976 119877 12099
Cusp forms 127945 117067 10878
Eisenstein series 4031 2810 1221

## Trace form

 $$117067 q - 303 q^{2} - 302 q^{3} - 299 q^{4} - 458 q^{5} - 906 q^{6} - 298 q^{7} - 291 q^{8} - 293 q^{9} + O(q^{10})$$ $$117067 q - 303 q^{2} - 302 q^{3} - 299 q^{4} - 458 q^{5} - 906 q^{6} - 298 q^{7} - 291 q^{8} - 293 q^{9} - 456 q^{10} - 906 q^{11} - 326 q^{12} - 340 q^{13} - 354 q^{14} - 491 q^{15} - 1031 q^{16} - 324 q^{17} - 411 q^{18} - 366 q^{19} - 956 q^{20} - 970 q^{21} - 378 q^{22} - 318 q^{23} - 390 q^{24} - 494 q^{25} - 948 q^{26} - 350 q^{27} - 406 q^{28} - 348 q^{29} - 573 q^{30} - 958 q^{31} - 423 q^{32} - 474 q^{33} - 432 q^{34} - 523 q^{35} - 1259 q^{36} - 376 q^{37} - 450 q^{38} - 754 q^{39} - 606 q^{40} - 948 q^{41} - 570 q^{42} - 418 q^{43} - 510 q^{44} - 608 q^{45} - 1170 q^{46} - 438 q^{47} - 686 q^{48} - 405 q^{49} - 654 q^{50} - 1062 q^{51} - 472 q^{52} - 396 q^{53} - 510 q^{54} - 519 q^{55} - 1266 q^{56} - 414 q^{57} - 648 q^{58} - 426 q^{59} - 737 q^{60} - 1120 q^{61} - 606 q^{62} - 538 q^{63} - 731 q^{64} - 643 q^{65} - 1350 q^{66} - 610 q^{67} - 684 q^{68} - 606 q^{69} - 723 q^{70} - 1098 q^{71} - 615 q^{72} - 568 q^{73} - 552 q^{74} - 521 q^{75} - 1152 q^{76} - 822 q^{77} - 426 q^{78} - 490 q^{79} - 320 q^{80} - 977 q^{81} - 576 q^{82} - 258 q^{83} - 82 q^{84} - 369 q^{85} - 894 q^{86} - 186 q^{87} - 54 q^{88} - 324 q^{89} - 114 q^{90} - 854 q^{91} - 30 q^{92} - 10 q^{93} + 18 q^{94} - 441 q^{95} - 1242 q^{96} - 244 q^{97} - 243 q^{98} - 114 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1805))$$

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
1805.2.a $$\chi_{1805}(1, \cdot)$$ 1805.2.a.a 1 1
1805.2.a.b 1
1805.2.a.c 2
1805.2.a.d 2
1805.2.a.e 2
1805.2.a.f 3
1805.2.a.g 3
1805.2.a.h 3
1805.2.a.i 4
1805.2.a.j 4
1805.2.a.k 4
1805.2.a.l 4
1805.2.a.m 4
1805.2.a.n 4
1805.2.a.o 4
1805.2.a.p 4
1805.2.a.q 6
1805.2.a.r 6
1805.2.a.s 9
1805.2.a.t 9
1805.2.a.u 9
1805.2.a.v 9
1805.2.a.w 16
1805.2.b $$\chi_{1805}(1084, \cdot)$$ 1805.2.b.a 2 1
1805.2.b.b 2
1805.2.b.c 2
1805.2.b.d 2
1805.2.b.e 6
1805.2.b.f 6
1805.2.b.g 6
1805.2.b.h 8
1805.2.b.i 16
1805.2.b.j 16
1805.2.b.k 24
1805.2.b.l 24
1805.2.b.m 40
1805.2.e $$\chi_{1805}(1151, \cdot)$$ n/a 224 2
1805.2.g $$\chi_{1805}(1082, \cdot)$$ n/a 308 2
1805.2.i $$\chi_{1805}(429, \cdot)$$ n/a 308 2
1805.2.k $$\chi_{1805}(606, \cdot)$$ n/a 684 6
1805.2.l $$\chi_{1805}(293, \cdot)$$ n/a 616 4
1805.2.p $$\chi_{1805}(54, \cdot)$$ n/a 924 6
1805.2.q $$\chi_{1805}(96, \cdot)$$ n/a 2304 18
1805.2.s $$\chi_{1805}(127, \cdot)$$ n/a 1848 12
1805.2.v $$\chi_{1805}(39, \cdot)$$ n/a 3384 18
1805.2.w $$\chi_{1805}(11, \cdot)$$ n/a 4608 36
1805.2.x $$\chi_{1805}(18, \cdot)$$ n/a 6768 36
1805.2.ba $$\chi_{1805}(49, \cdot)$$ n/a 6768 36
1805.2.bc $$\chi_{1805}(6, \cdot)$$ n/a 13608 108
1805.2.be $$\chi_{1805}(8, \cdot)$$ n/a 13536 72
1805.2.bf $$\chi_{1805}(4, \cdot)$$ n/a 20304 108
1805.2.bi $$\chi_{1805}(2, \cdot)$$ n/a 40608 216

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1805))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1805)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 2}$$