# Properties

 Label 2156.4 Level 2156 Weight 4 Dimension 232163 Nonzero newspaces 32 Sturm bound 1128960 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$2156 = 2^{2} \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$32$$ Sturm bound: $$1128960$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2156))$$.

Total New Old
Modular forms 426360 233911 192449
Cusp forms 420360 232163 188197
Eisenstein series 6000 1748 4252

## Trace form

 $$232163 q - 125 q^{2} - 24 q^{3} - 125 q^{4} - 202 q^{5} - 113 q^{6} + 48 q^{7} - 17 q^{8} - 2 q^{9} + O(q^{10})$$ $$232163 q - 125 q^{2} - 24 q^{3} - 125 q^{4} - 202 q^{5} - 113 q^{6} + 48 q^{7} - 17 q^{8} - 2 q^{9} - 156 q^{10} - 118 q^{11} - 940 q^{12} - 806 q^{13} - 456 q^{14} - 658 q^{15} - 281 q^{16} - 156 q^{17} - 254 q^{18} + 1047 q^{19} - 588 q^{20} + 1008 q^{21} - 614 q^{22} - 144 q^{23} + 829 q^{24} - 2854 q^{25} + 1446 q^{26} - 2283 q^{27} + 1152 q^{28} - 3344 q^{29} + 4372 q^{30} + 2334 q^{31} + 3240 q^{32} + 3337 q^{33} - 1208 q^{34} + 996 q^{35} - 4626 q^{36} + 6718 q^{37} - 6268 q^{38} + 1490 q^{39} - 5220 q^{40} - 5584 q^{41} - 4146 q^{42} - 5278 q^{43} - 2793 q^{44} - 16182 q^{45} - 3410 q^{46} - 5356 q^{47} + 1110 q^{48} - 7644 q^{49} + 6091 q^{50} - 2207 q^{51} + 11870 q^{52} + 6414 q^{53} + 18180 q^{54} + 5984 q^{55} + 6756 q^{56} + 11811 q^{57} + 8748 q^{58} + 8393 q^{59} + 5644 q^{60} + 17638 q^{61} - 4088 q^{62} + 16716 q^{63} - 11045 q^{64} + 6880 q^{65} - 12903 q^{66} - 5198 q^{67} - 28284 q^{68} - 7264 q^{69} - 14826 q^{70} - 9504 q^{71} - 29627 q^{72} - 15028 q^{73} - 9654 q^{74} - 38957 q^{75} - 168 q^{76} - 10350 q^{77} + 10618 q^{78} - 13578 q^{79} + 9186 q^{80} - 54859 q^{81} + 7615 q^{82} - 18199 q^{83} - 18072 q^{84} - 4994 q^{85} + 22357 q^{86} + 2260 q^{87} + 15583 q^{88} - 7558 q^{89} + 42690 q^{90} + 17280 q^{91} + 13962 q^{92} + 54268 q^{93} + 12182 q^{94} + 46970 q^{95} + 26306 q^{96} + 23591 q^{97} + 37380 q^{98} + 15634 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2156))$$

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
2156.4.a $$\chi_{2156}(1, \cdot)$$ 2156.4.a.a 1 1
2156.4.a.b 1
2156.4.a.c 1
2156.4.a.d 2
2156.4.a.e 3
2156.4.a.f 4
2156.4.a.g 5
2156.4.a.h 6
2156.4.a.i 8
2156.4.a.j 10
2156.4.a.k 10
2156.4.a.l 10
2156.4.a.m 10
2156.4.a.n 14
2156.4.a.o 18
2156.4.c $$\chi_{2156}(1077, \cdot)$$ n/a 120 1
2156.4.d $$\chi_{2156}(1275, \cdot)$$ n/a 728 1
2156.4.f $$\chi_{2156}(1959, \cdot)$$ n/a 600 1
2156.4.i $$\chi_{2156}(177, \cdot)$$ n/a 200 2
2156.4.j $$\chi_{2156}(785, \cdot)$$ n/a 492 4
2156.4.l $$\chi_{2156}(815, \cdot)$$ n/a 1200 2
2156.4.n $$\chi_{2156}(263, \cdot)$$ n/a 1424 2
2156.4.q $$\chi_{2156}(901, \cdot)$$ n/a 240 2
2156.4.r $$\chi_{2156}(309, \cdot)$$ n/a 840 6
2156.4.u $$\chi_{2156}(587, \cdot)$$ n/a 2848 4
2156.4.w $$\chi_{2156}(491, \cdot)$$ n/a 2912 4
2156.4.x $$\chi_{2156}(293, \cdot)$$ n/a 480 4
2156.4.bb $$\chi_{2156}(111, \cdot)$$ n/a 5040 6
2156.4.bd $$\chi_{2156}(43, \cdot)$$ n/a 6024 6
2156.4.be $$\chi_{2156}(153, \cdot)$$ n/a 1008 6
2156.4.bg $$\chi_{2156}(361, \cdot)$$ n/a 960 8
2156.4.bh $$\chi_{2156}(221, \cdot)$$ n/a 1680 12
2156.4.bi $$\chi_{2156}(117, \cdot)$$ n/a 960 8
2156.4.bl $$\chi_{2156}(79, \cdot)$$ n/a 5696 8
2156.4.bn $$\chi_{2156}(31, \cdot)$$ n/a 5696 8
2156.4.bp $$\chi_{2156}(113, \cdot)$$ n/a 4032 24
2156.4.bq $$\chi_{2156}(241, \cdot)$$ n/a 2016 12
2156.4.bt $$\chi_{2156}(219, \cdot)$$ n/a 12048 12
2156.4.bv $$\chi_{2156}(199, \cdot)$$ n/a 10080 12
2156.4.by $$\chi_{2156}(13, \cdot)$$ n/a 4032 24
2156.4.bz $$\chi_{2156}(127, \cdot)$$ n/a 24096 24
2156.4.cb $$\chi_{2156}(27, \cdot)$$ n/a 24096 24
2156.4.ce $$\chi_{2156}(9, \cdot)$$ n/a 8064 48
2156.4.cg $$\chi_{2156}(3, \cdot)$$ n/a 48192 48
2156.4.ci $$\chi_{2156}(39, \cdot)$$ n/a 48192 48
2156.4.cl $$\chi_{2156}(17, \cdot)$$ n/a 8064 48

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2156))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2156)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(154))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(308))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(1078))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2156))$$$$^{\oplus 1}$$