# Properties

 Label 1859.4 Level 1859 Weight 4 Dimension 412000 Nonzero newspaces 24 Sturm bound 1135680 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$1859 = 11 \cdot 13^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$24$$ Sturm bound: $$1135680$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1859))$$.

Total New Old
Modular forms 428160 415680 12480
Cusp forms 423600 412000 11600
Eisenstein series 4560 3680 880

## Trace form

 $$412000 q - 533 q^{2} - 533 q^{3} - 533 q^{4} - 533 q^{5} - 583 q^{6} - 687 q^{7} - 781 q^{8} - 453 q^{9} + O(q^{10})$$ $$412000 q - 533 q^{2} - 533 q^{3} - 533 q^{4} - 533 q^{5} - 583 q^{6} - 687 q^{7} - 781 q^{8} - 453 q^{9} - 78 q^{10} - 429 q^{11} - 102 q^{12} - 288 q^{13} - 728 q^{14} - 555 q^{15} - 913 q^{16} - 1439 q^{17} - 3850 q^{18} - 2084 q^{19} - 2162 q^{20} - 118 q^{21} + 811 q^{22} - 386 q^{23} + 3501 q^{24} + 883 q^{25} + 924 q^{26} + 2194 q^{27} - 914 q^{28} - 2299 q^{29} - 3212 q^{30} - 2171 q^{31} - 2924 q^{32} - 2004 q^{33} - 4322 q^{34} - 463 q^{35} - 1112 q^{36} + 339 q^{37} + 5300 q^{38} - 432 q^{39} - 1832 q^{40} - 1907 q^{41} - 3018 q^{42} - 2918 q^{43} - 1246 q^{44} + 832 q^{45} + 3674 q^{46} + 585 q^{47} - 644 q^{48} + 4345 q^{49} - 827 q^{50} - 2498 q^{51} - 1236 q^{52} + 799 q^{53} - 834 q^{54} + 609 q^{55} + 1380 q^{56} + 2718 q^{57} + 4776 q^{58} + 2750 q^{59} + 5804 q^{60} - 4737 q^{61} - 8402 q^{62} - 13068 q^{63} - 18577 q^{64} - 8694 q^{65} - 8114 q^{66} - 3996 q^{67} + 6126 q^{68} + 8504 q^{69} + 7556 q^{70} + 7713 q^{71} + 11431 q^{72} + 5557 q^{73} + 8298 q^{74} + 1264 q^{75} - 7682 q^{76} - 2073 q^{77} + 4596 q^{78} - 5393 q^{79} + 9572 q^{80} + 10719 q^{82} + 13720 q^{83} + 7748 q^{84} + 6375 q^{85} - 10831 q^{86} - 12618 q^{87} + 3205 q^{88} - 14128 q^{89} - 28398 q^{90} - 6024 q^{91} - 22698 q^{92} - 19995 q^{93} - 7682 q^{94} - 6717 q^{95} + 5988 q^{96} + 7570 q^{97} - 9554 q^{98} + 11413 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1859))$$

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
1859.4.a $$\chi_{1859}(1, \cdot)$$ 1859.4.a.a 2 1
1859.4.a.b 4
1859.4.a.c 6
1859.4.a.d 9
1859.4.a.e 11
1859.4.a.f 17
1859.4.a.g 17
1859.4.a.h 17
1859.4.a.i 17
1859.4.a.j 18
1859.4.a.k 18
1859.4.a.l 36
1859.4.a.m 36
1859.4.a.n 39
1859.4.a.o 39
1859.4.a.p 51
1859.4.a.q 51
1859.4.b $$\chi_{1859}(1013, \cdot)$$ n/a 384 1
1859.4.e $$\chi_{1859}(529, \cdot)$$ n/a 772 2
1859.4.g $$\chi_{1859}(1253, \cdot)$$ n/a 904 2
1859.4.h $$\chi_{1859}(170, \cdot)$$ n/a 1816 4
1859.4.j $$\chi_{1859}(23, \cdot)$$ n/a 768 2
1859.4.n $$\chi_{1859}(168, \cdot)$$ n/a 1808 4
1859.4.o $$\chi_{1859}(934, \cdot)$$ n/a 1808 4
1859.4.q $$\chi_{1859}(144, \cdot)$$ n/a 5448 12
1859.4.r $$\chi_{1859}(146, \cdot)$$ n/a 3616 8
1859.4.t $$\chi_{1859}(239, \cdot)$$ n/a 3616 8
1859.4.w $$\chi_{1859}(12, \cdot)$$ n/a 5472 12
1859.4.y $$\chi_{1859}(147, \cdot)$$ n/a 3616 8
1859.4.ba $$\chi_{1859}(100, \cdot)$$ n/a 10896 24
1859.4.bb $$\chi_{1859}(21, \cdot)$$ n/a 13056 24
1859.4.bd $$\chi_{1859}(19, \cdot)$$ n/a 7232 16
1859.4.bf $$\chi_{1859}(14, \cdot)$$ n/a 26112 48
1859.4.bh $$\chi_{1859}(56, \cdot)$$ n/a 10944 24
1859.4.bj $$\chi_{1859}(25, \cdot)$$ n/a 26112 48
1859.4.bn $$\chi_{1859}(32, \cdot)$$ n/a 26112 48
1859.4.bo $$\chi_{1859}(3, \cdot)$$ n/a 52224 96
1859.4.bp $$\chi_{1859}(8, \cdot)$$ n/a 52224 96
1859.4.bs $$\chi_{1859}(4, \cdot)$$ n/a 52224 96
1859.4.bv $$\chi_{1859}(2, \cdot)$$ n/a 104448 192

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1859))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1859)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 2}$$