# Properties

 Label 882.4 Level 882 Weight 4 Dimension 16081 Nonzero newspaces 20 Sturm bound 169344 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$20$$ Sturm bound: $$169344$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(882))$$.

Total New Old
Modular forms 64464 16081 48383
Cusp forms 62544 16081 46463
Eisenstein series 1920 0 1920

## Trace form

 $$16081 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 60 q^{5} - 18 q^{6} + 48 q^{7} - 8 q^{8} - 105 q^{9} + O(q^{10})$$ $$16081 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 60 q^{5} - 18 q^{6} + 48 q^{7} - 8 q^{8} - 105 q^{9} - 84 q^{10} - 57 q^{11} + 24 q^{12} + 458 q^{13} + 396 q^{14} + 570 q^{15} - 32 q^{16} - 804 q^{17} - 516 q^{18} - 1666 q^{19} - 672 q^{20} - 720 q^{21} - 1338 q^{22} - 1860 q^{23} - 216 q^{24} - 728 q^{25} - 52 q^{26} + 1584 q^{27} + 168 q^{28} + 3462 q^{29} + 1392 q^{30} + 4238 q^{31} + 64 q^{32} + 2253 q^{33} + 1158 q^{34} + 492 q^{35} + 516 q^{36} + 3050 q^{37} + 2750 q^{38} - 3102 q^{39} + 672 q^{40} - 5865 q^{41} - 4147 q^{43} - 1872 q^{44} - 3486 q^{45} - 4788 q^{46} - 5976 q^{47} - 144 q^{48} - 4854 q^{49} - 7988 q^{50} - 6705 q^{51} + 848 q^{52} + 750 q^{53} - 486 q^{54} + 936 q^{55} + 288 q^{56} + 7131 q^{57} - 312 q^{58} + 12069 q^{59} + 7128 q^{60} - 1816 q^{61} + 9500 q^{62} + 10416 q^{63} - 320 q^{64} + 13626 q^{65} + 9888 q^{66} + 1883 q^{67} + 4164 q^{68} + 9342 q^{69} + 396 q^{70} + 6528 q^{71} - 24 q^{72} + 6188 q^{73} - 6700 q^{74} - 20121 q^{75} + 1532 q^{76} - 9522 q^{77} - 16956 q^{78} - 2758 q^{79} + 96 q^{80} - 1533 q^{81} - 1032 q^{82} - 2094 q^{83} - 3948 q^{85} + 9554 q^{86} + 6228 q^{87} + 5208 q^{88} + 19482 q^{89} + 9744 q^{90} + 450 q^{91} + 4128 q^{92} + 2406 q^{93} + 3588 q^{94} - 11628 q^{95} - 384 q^{96} - 9757 q^{97} - 6288 q^{98} - 5520 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(882))$$

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
882.4.a $$\chi_{882}(1, \cdot)$$ 882.4.a.a 1 1
882.4.a.b 1
882.4.a.c 1
882.4.a.d 1
882.4.a.e 1
882.4.a.f 1
882.4.a.g 1
882.4.a.h 1
882.4.a.i 1
882.4.a.j 1
882.4.a.k 1
882.4.a.l 1
882.4.a.m 1
882.4.a.n 1
882.4.a.o 1
882.4.a.p 1
882.4.a.q 1
882.4.a.r 1
882.4.a.s 1
882.4.a.t 2
882.4.a.u 2
882.4.a.v 2
882.4.a.w 2
882.4.a.x 2
882.4.a.y 2
882.4.a.z 2
882.4.a.ba 2
882.4.a.bb 2
882.4.a.bc 2
882.4.a.bd 2
882.4.a.be 2
882.4.a.bf 2
882.4.a.bg 2
882.4.a.bh 2
882.4.a.bi 2
882.4.d $$\chi_{882}(881, \cdot)$$ 882.4.d.a 8 1
882.4.d.b 16
882.4.d.c 16
882.4.e $$\chi_{882}(373, \cdot)$$ n/a 240 2
882.4.f $$\chi_{882}(295, \cdot)$$ n/a 246 2
882.4.g $$\chi_{882}(361, \cdot)$$ 882.4.g.a 2 2
882.4.g.b 2
882.4.g.c 2
882.4.g.d 2
882.4.g.e 2
882.4.g.f 2
882.4.g.g 2
882.4.g.h 2
882.4.g.i 2
882.4.g.j 2
882.4.g.k 2
882.4.g.l 2
882.4.g.m 2
882.4.g.n 2
882.4.g.o 2
882.4.g.p 2
882.4.g.q 2
882.4.g.r 2
882.4.g.s 2
882.4.g.t 2
882.4.g.u 2
882.4.g.v 2
882.4.g.w 2
882.4.g.x 2
882.4.g.y 4
882.4.g.z 4
882.4.g.ba 4
882.4.g.bb 4
882.4.g.bc 4
882.4.g.bd 4
882.4.g.be 4
882.4.g.bf 4
882.4.g.bg 4
882.4.g.bh 4
882.4.g.bi 4
882.4.g.bj 4
882.4.g.bk 4
882.4.h $$\chi_{882}(67, \cdot)$$ n/a 240 2
882.4.k $$\chi_{882}(215, \cdot)$$ 882.4.k.a 16 2
882.4.k.b 16
882.4.k.c 16
882.4.k.d 32
882.4.l $$\chi_{882}(227, \cdot)$$ n/a 240 2
882.4.m $$\chi_{882}(293, \cdot)$$ n/a 240 2
882.4.t $$\chi_{882}(803, \cdot)$$ n/a 240 2
882.4.u $$\chi_{882}(127, \cdot)$$ n/a 420 6
882.4.v $$\chi_{882}(125, \cdot)$$ n/a 336 6
882.4.y $$\chi_{882}(193, \cdot)$$ n/a 2016 12
882.4.z $$\chi_{882}(37, \cdot)$$ n/a 840 12
882.4.ba $$\chi_{882}(43, \cdot)$$ n/a 2016 12
882.4.bb $$\chi_{882}(25, \cdot)$$ n/a 2016 12
882.4.bc $$\chi_{882}(47, \cdot)$$ n/a 2016 12
882.4.bj $$\chi_{882}(41, \cdot)$$ n/a 2016 12
882.4.bk $$\chi_{882}(5, \cdot)$$ n/a 2016 12
882.4.bl $$\chi_{882}(17, \cdot)$$ n/a 672 12

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(882))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(882)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(882))$$$$^{\oplus 1}$$