# Properties

 Label 1936.4 Level 1936 Weight 4 Dimension 192161 Nonzero newspaces 16 Sturm bound 929280 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$1936 = 2^{4} \cdot 11^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$929280$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1936))$$.

Total New Old
Modular forms 350720 193426 157294
Cusp forms 346240 192161 154079
Eisenstein series 4480 1265 3215

## Trace form

 $$192161 q - 182 q^{2} - 133 q^{3} - 172 q^{4} - 229 q^{5} - 212 q^{6} - 159 q^{7} - 224 q^{8} - 56 q^{9} + O(q^{10})$$ $$192161 q - 182 q^{2} - 133 q^{3} - 172 q^{4} - 229 q^{5} - 212 q^{6} - 159 q^{7} - 224 q^{8} - 56 q^{9} - 248 q^{10} - 150 q^{11} - 240 q^{12} - 205 q^{13} + 8 q^{14} - 267 q^{15} + 100 q^{16} - 359 q^{17} - 6 q^{18} - 205 q^{19} - 376 q^{20} - 259 q^{21} - 200 q^{22} - 199 q^{23} - 1028 q^{24} - 166 q^{25} - 444 q^{26} - 103 q^{27} + 100 q^{28} - 229 q^{29} + 1056 q^{30} + 393 q^{31} + 788 q^{32} + 890 q^{33} + 96 q^{34} + 2129 q^{35} - 776 q^{36} - 437 q^{37} - 1412 q^{38} - 2807 q^{39} - 1516 q^{40} - 3203 q^{41} - 860 q^{42} - 3615 q^{43} - 200 q^{44} - 5129 q^{45} + 952 q^{46} - 3467 q^{47} + 1588 q^{48} - 1118 q^{49} + 546 q^{50} + 125 q^{51} - 416 q^{52} + 1035 q^{53} - 1556 q^{54} + 2520 q^{55} - 828 q^{56} + 5339 q^{57} - 172 q^{58} + 2239 q^{59} - 372 q^{60} + 1235 q^{61} - 260 q^{62} + 2487 q^{63} + 332 q^{64} - 931 q^{65} - 200 q^{66} + 1499 q^{67} - 1060 q^{68} + 849 q^{69} - 13740 q^{70} - 4563 q^{71} - 29688 q^{72} - 19571 q^{73} - 19632 q^{74} - 9093 q^{75} - 15808 q^{76} - 2090 q^{77} - 2552 q^{78} - 2395 q^{79} + 10812 q^{80} + 10566 q^{81} + 21916 q^{82} + 3767 q^{83} + 37780 q^{84} + 25583 q^{85} + 30784 q^{86} + 11047 q^{87} + 27640 q^{88} + 14229 q^{89} + 53556 q^{90} + 11669 q^{91} + 21892 q^{92} + 16463 q^{93} + 18172 q^{94} + 9953 q^{95} + 1388 q^{96} - 1607 q^{97} - 9986 q^{98} - 2400 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1936))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1936.4.a $$\chi_{1936}(1, \cdot)$$ 1936.4.a.a 1 1
1936.4.a.b 1
1936.4.a.c 1
1936.4.a.d 1
1936.4.a.e 1
1936.4.a.f 1
1936.4.a.g 1
1936.4.a.h 1
1936.4.a.i 1
1936.4.a.j 1
1936.4.a.k 1
1936.4.a.l 1
1936.4.a.m 1
1936.4.a.n 1
1936.4.a.o 2
1936.4.a.p 2
1936.4.a.q 2
1936.4.a.r 2
1936.4.a.s 2
1936.4.a.t 2
1936.4.a.u 2
1936.4.a.v 2
1936.4.a.w 2
1936.4.a.x 2
1936.4.a.y 2
1936.4.a.z 2
1936.4.a.ba 2
1936.4.a.bb 2
1936.4.a.bc 2
1936.4.a.bd 3
1936.4.a.be 3
1936.4.a.bf 3
1936.4.a.bg 3
1936.4.a.bh 3
1936.4.a.bi 3
1936.4.a.bj 3
1936.4.a.bk 4
1936.4.a.bl 4
1936.4.a.bm 4
1936.4.a.bn 4
1936.4.a.bo 4
1936.4.a.bp 4
1936.4.a.bq 6
1936.4.a.br 6
1936.4.a.bs 6
1936.4.a.bt 8
1936.4.a.bu 8
1936.4.a.bv 8
1936.4.a.bw 8
1936.4.a.bx 10
1936.4.a.by 10
1936.4.c $$\chi_{1936}(969, \cdot)$$ None 0 1
1936.4.e $$\chi_{1936}(1935, \cdot)$$ n/a 162 1
1936.4.g $$\chi_{1936}(967, \cdot)$$ None 0 1
1936.4.i $$\chi_{1936}(483, \cdot)$$ n/a 1280 2
1936.4.j $$\chi_{1936}(485, \cdot)$$ n/a 1290 2
1936.4.m $$\chi_{1936}(81, \cdot)$$ n/a 632 4
1936.4.o $$\chi_{1936}(215, \cdot)$$ None 0 4
1936.4.q $$\chi_{1936}(239, \cdot)$$ n/a 648 4
1936.4.s $$\chi_{1936}(9, \cdot)$$ None 0 4
1936.4.u $$\chi_{1936}(177, \cdot)$$ n/a 1970 10
1936.4.x $$\chi_{1936}(245, \cdot)$$ n/a 5120 8
1936.4.y $$\chi_{1936}(403, \cdot)$$ n/a 5120 8
1936.4.z $$\chi_{1936}(175, \cdot)$$ n/a 1980 10
1936.4.bb $$\chi_{1936}(89, \cdot)$$ None 0 10
1936.4.be $$\chi_{1936}(87, \cdot)$$ None 0 10
1936.4.bi $$\chi_{1936}(45, \cdot)$$ n/a 15800 20
1936.4.bj $$\chi_{1936}(43, \cdot)$$ n/a 15800 20
1936.4.bk $$\chi_{1936}(49, \cdot)$$ n/a 7880 40
1936.4.bm $$\chi_{1936}(7, \cdot)$$ None 0 40
1936.4.bp $$\chi_{1936}(25, \cdot)$$ None 0 40
1936.4.br $$\chi_{1936}(63, \cdot)$$ n/a 7920 40
1936.4.bs $$\chi_{1936}(19, \cdot)$$ n/a 63200 80
1936.4.bt $$\chi_{1936}(5, \cdot)$$ n/a 63200 80

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1936))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1936)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 15}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 10}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 5}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(484))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(968))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1936))$$$$^{\oplus 1}$$