## Defining parameters

 Level: $$N$$ = $$1856 = 2^{6} \cdot 29$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$28$$ Sturm bound: $$860160$$ Trace bound: $$15$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1856))$$.

Total New Old
Modular forms 324576 181602 142974
Cusp forms 320544 180414 140130
Eisenstein series 4032 1188 2844

## Trace form

 $$180414 q - 208 q^{2} - 156 q^{3} - 208 q^{4} - 208 q^{5} - 208 q^{6} - 152 q^{7} - 208 q^{8} - 206 q^{9} + O(q^{10})$$ $$180414 q - 208 q^{2} - 156 q^{3} - 208 q^{4} - 208 q^{5} - 208 q^{6} - 152 q^{7} - 208 q^{8} - 206 q^{9} - 208 q^{10} - 116 q^{11} - 208 q^{12} - 352 q^{13} - 208 q^{14} - 400 q^{15} - 208 q^{16} - 572 q^{17} - 208 q^{18} - 204 q^{19} - 208 q^{20} - 184 q^{21} - 1152 q^{22} - 152 q^{23} - 2208 q^{24} - 362 q^{25} - 128 q^{26} + 216 q^{27} + 1312 q^{28} + 184 q^{29} + 4208 q^{30} + 568 q^{31} + 2272 q^{32} + 1808 q^{33} + 1792 q^{34} + 800 q^{35} + 1552 q^{36} + 832 q^{37} - 1088 q^{38} - 152 q^{39} - 3488 q^{40} - 2308 q^{41} - 6528 q^{42} - 1828 q^{43} - 2208 q^{44} - 3176 q^{45} - 208 q^{46} - 2040 q^{47} - 208 q^{48} - 2490 q^{49} + 5504 q^{50} - 9104 q^{51} + 6416 q^{52} - 1024 q^{53} + 3248 q^{54} - 1304 q^{55} - 992 q^{56} + 1896 q^{57} - 2592 q^{58} + 8596 q^{59} - 10000 q^{60} + 1952 q^{61} - 6192 q^{62} + 15200 q^{63} - 12304 q^{64} + 3976 q^{65} - 11280 q^{66} + 11892 q^{67} - 4336 q^{68} + 1064 q^{69} - 4240 q^{70} + 744 q^{71} + 1088 q^{72} - 2308 q^{73} + 5056 q^{74} - 14892 q^{75} + 11696 q^{76} - 6456 q^{77} + 3776 q^{78} - 20312 q^{79} - 8736 q^{80} - 14002 q^{81} - 14128 q^{82} - 5276 q^{83} - 8496 q^{84} - 3520 q^{85} + 832 q^{86} - 160 q^{87} + 5808 q^{88} + 6876 q^{89} + 18512 q^{90} + 6512 q^{91} + 25024 q^{92} + 16544 q^{93} + 17648 q^{94} + 13632 q^{95} + 25632 q^{96} + 18548 q^{97} + 24000 q^{98} + 9332 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1856))$$

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
1856.4.a $$\chi_{1856}(1, \cdot)$$ 1856.4.a.a 1 1
1856.4.a.b 1
1856.4.a.c 1
1856.4.a.d 1
1856.4.a.e 1
1856.4.a.f 1
1856.4.a.g 2
1856.4.a.h 2
1856.4.a.i 2
1856.4.a.j 2
1856.4.a.k 2
1856.4.a.l 2
1856.4.a.m 2
1856.4.a.n 2
1856.4.a.o 3
1856.4.a.p 3
1856.4.a.q 3
1856.4.a.r 3
1856.4.a.s 3
1856.4.a.t 3
1856.4.a.u 3
1856.4.a.v 3
1856.4.a.w 4
1856.4.a.x 4
1856.4.a.y 5
1856.4.a.z 5
1856.4.a.ba 5
1856.4.a.bb 5
1856.4.a.bc 6
1856.4.a.bd 6
1856.4.a.be 8
1856.4.a.bf 9
1856.4.a.bg 9
1856.4.a.bh 10
1856.4.a.bi 10
1856.4.a.bj 12
1856.4.a.bk 12
1856.4.a.bl 12
1856.4.c $$\chi_{1856}(929, \cdot)$$ n/a 168 1
1856.4.e $$\chi_{1856}(1217, \cdot)$$ n/a 178 1
1856.4.g $$\chi_{1856}(289, \cdot)$$ n/a 180 1
1856.4.j $$\chi_{1856}(911, \cdot)$$ n/a 356 2
1856.4.k $$\chi_{1856}(191, \cdot)$$ n/a 356 2
1856.4.m $$\chi_{1856}(753, \cdot)$$ n/a 356 2
1856.4.n $$\chi_{1856}(465, \cdot)$$ n/a 336 2
1856.4.q $$\chi_{1856}(1119, \cdot)$$ n/a 360 2
1856.4.t $$\chi_{1856}(655, \cdot)$$ n/a 356 2
1856.4.u $$\chi_{1856}(65, \cdot)$$ n/a 1068 6
1856.4.v $$\chi_{1856}(233, \cdot)$$ None 0 4
1856.4.x $$\chi_{1856}(679, \cdot)$$ None 0 4
1856.4.ba $$\chi_{1856}(215, \cdot)$$ None 0 4
1856.4.bc $$\chi_{1856}(57, \cdot)$$ None 0 4
1856.4.be $$\chi_{1856}(33, \cdot)$$ n/a 1080 6
1856.4.bg $$\chi_{1856}(129, \cdot)$$ n/a 1068 6
1856.4.bi $$\chi_{1856}(161, \cdot)$$ n/a 1080 6
1856.4.bl $$\chi_{1856}(307, \cdot)$$ n/a 5744 8
1856.4.bn $$\chi_{1856}(117, \cdot)$$ n/a 5376 8
1856.4.bp $$\chi_{1856}(173, \cdot)$$ n/a 5744 8
1856.4.bq $$\chi_{1856}(75, \cdot)$$ n/a 5744 8
1856.4.bs $$\chi_{1856}(47, \cdot)$$ n/a 2136 12
1856.4.bv $$\chi_{1856}(31, \cdot)$$ n/a 2160 12
1856.4.by $$\chi_{1856}(49, \cdot)$$ n/a 2136 12
1856.4.bz $$\chi_{1856}(209, \cdot)$$ n/a 2136 12
1856.4.cb $$\chi_{1856}(127, \cdot)$$ n/a 2136 12
1856.4.cc $$\chi_{1856}(15, \cdot)$$ n/a 2136 12
1856.4.cf $$\chi_{1856}(9, \cdot)$$ None 0 24
1856.4.ch $$\chi_{1856}(55, \cdot)$$ None 0 24
1856.4.ci $$\chi_{1856}(39, \cdot)$$ None 0 24
1856.4.ck $$\chi_{1856}(25, \cdot)$$ None 0 24
1856.4.cm $$\chi_{1856}(11, \cdot)$$ n/a 34464 48
1856.4.co $$\chi_{1856}(5, \cdot)$$ n/a 34464 48
1856.4.cq $$\chi_{1856}(45, \cdot)$$ n/a 34464 48
1856.4.ct $$\chi_{1856}(3, \cdot)$$ n/a 34464 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1856))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1856)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 7}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(232))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(928))$$$$^{\oplus 2}$$