# Properties

 Label 1617.4 Level 1617 Weight 4 Dimension 198872 Nonzero newspaces 32 Sturm bound 752640 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1617 = 3 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$32$$ Sturm bound: $$752640$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1617))$$.

Total New Old
Modular forms 284640 200620 84020
Cusp forms 279840 198872 80968
Eisenstein series 4800 1748 3052

## Trace form

 $$198872 q - 101 q^{3} - 250 q^{4} - 96 q^{5} - 207 q^{6} - 384 q^{7} + 136 q^{8} - 37 q^{9} + O(q^{10})$$ $$198872 q - 101 q^{3} - 250 q^{4} - 96 q^{5} - 207 q^{6} - 384 q^{7} + 136 q^{8} - 37 q^{9} - 224 q^{10} - 100 q^{11} - 812 q^{12} - 602 q^{13} - 624 q^{14} - 679 q^{15} + 30 q^{16} + 252 q^{17} + 1107 q^{18} + 1556 q^{19} + 3226 q^{20} + 1032 q^{21} - 868 q^{22} - 1052 q^{23} - 547 q^{24} - 2290 q^{25} - 1226 q^{26} - 515 q^{27} - 2496 q^{28} - 1892 q^{29} - 4298 q^{30} - 1846 q^{31} - 3092 q^{32} + 69 q^{33} + 240 q^{34} + 168 q^{35} + 2055 q^{36} - 3986 q^{37} - 4226 q^{38} - 451 q^{39} - 8188 q^{40} - 2796 q^{41} + 5514 q^{42} + 7088 q^{43} + 10654 q^{44} + 8690 q^{45} + 21984 q^{46} + 9716 q^{47} + 8340 q^{48} + 11160 q^{49} + 994 q^{50} - 6378 q^{51} + 840 q^{52} - 3376 q^{53} - 17280 q^{54} + 352 q^{55} - 2652 q^{56} - 1968 q^{57} - 1916 q^{58} - 12780 q^{59} - 18806 q^{60} - 27362 q^{61} - 44664 q^{62} - 7380 q^{63} - 34114 q^{64} - 14784 q^{65} - 7545 q^{66} + 3116 q^{67} + 1616 q^{68} + 2578 q^{69} + 4956 q^{70} + 21972 q^{71} + 23902 q^{72} + 10970 q^{73} + 24630 q^{74} + 25116 q^{75} + 64688 q^{76} + 13500 q^{77} + 21958 q^{78} + 19334 q^{79} + 26706 q^{80} + 5495 q^{81} - 21014 q^{82} - 16648 q^{83} - 16296 q^{84} - 12026 q^{85} - 15956 q^{86} - 13272 q^{87} - 52258 q^{88} - 21308 q^{89} - 14990 q^{90} - 4308 q^{91} - 47090 q^{92} + 6993 q^{93} + 23900 q^{94} + 38208 q^{95} + 40678 q^{96} + 39452 q^{97} + 102108 q^{98} + 11513 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1617))$$

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
1617.4.a $$\chi_{1617}(1, \cdot)$$ 1617.4.a.a 1 1
1617.4.a.b 1
1617.4.a.c 1
1617.4.a.d 1
1617.4.a.e 1
1617.4.a.f 1
1617.4.a.g 1
1617.4.a.h 2
1617.4.a.i 2
1617.4.a.j 2
1617.4.a.k 2
1617.4.a.l 2
1617.4.a.m 2
1617.4.a.n 5
1617.4.a.o 5
1617.4.a.p 5
1617.4.a.q 7
1617.4.a.r 7
1617.4.a.s 7
1617.4.a.t 7
1617.4.a.u 8
1617.4.a.v 8
1617.4.a.w 10
1617.4.a.x 10
1617.4.a.y 10
1617.4.a.z 10
1617.4.a.ba 12
1617.4.a.bb 12
1617.4.a.bc 16
1617.4.a.bd 16
1617.4.a.be 16
1617.4.a.bf 16
1617.4.c $$\chi_{1617}(538, \cdot)$$ n/a 240 1
1617.4.e $$\chi_{1617}(881, \cdot)$$ n/a 400 1
1617.4.g $$\chi_{1617}(197, \cdot)$$ n/a 482 1
1617.4.i $$\chi_{1617}(67, \cdot)$$ n/a 400 2
1617.4.j $$\chi_{1617}(148, \cdot)$$ n/a 984 4
1617.4.l $$\chi_{1617}(263, \cdot)$$ n/a 944 2
1617.4.n $$\chi_{1617}(815, \cdot)$$ n/a 800 2
1617.4.p $$\chi_{1617}(472, \cdot)$$ n/a 480 2
1617.4.r $$\chi_{1617}(232, \cdot)$$ n/a 1680 6
1617.4.t $$\chi_{1617}(50, \cdot)$$ n/a 1928 4
1617.4.v $$\chi_{1617}(146, \cdot)$$ n/a 1888 4
1617.4.x $$\chi_{1617}(244, \cdot)$$ n/a 960 4
1617.4.ba $$\chi_{1617}(428, \cdot)$$ n/a 4008 6
1617.4.bc $$\chi_{1617}(188, \cdot)$$ n/a 3360 6
1617.4.be $$\chi_{1617}(76, \cdot)$$ n/a 2016 6
1617.4.bg $$\chi_{1617}(214, \cdot)$$ n/a 1920 8
1617.4.bh $$\chi_{1617}(100, \cdot)$$ n/a 3360 12
1617.4.bj $$\chi_{1617}(19, \cdot)$$ n/a 1920 8
1617.4.bl $$\chi_{1617}(80, \cdot)$$ n/a 3776 8
1617.4.bn $$\chi_{1617}(116, \cdot)$$ n/a 3776 8
1617.4.bp $$\chi_{1617}(64, \cdot)$$ n/a 8064 24
1617.4.br $$\chi_{1617}(10, \cdot)$$ n/a 4032 12
1617.4.bt $$\chi_{1617}(89, \cdot)$$ n/a 6720 12
1617.4.bv $$\chi_{1617}(32, \cdot)$$ n/a 8016 12
1617.4.by $$\chi_{1617}(13, \cdot)$$ n/a 8064 24
1617.4.ca $$\chi_{1617}(20, \cdot)$$ n/a 16032 24
1617.4.cc $$\chi_{1617}(8, \cdot)$$ n/a 16032 24
1617.4.ce $$\chi_{1617}(4, \cdot)$$ n/a 16128 48
1617.4.cg $$\chi_{1617}(2, \cdot)$$ n/a 32064 48
1617.4.ci $$\chi_{1617}(5, \cdot)$$ n/a 32064 48
1617.4.ck $$\chi_{1617}(40, \cdot)$$ n/a 16128 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1617))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(1617)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1617))$$$$^{\oplus 1}$$