## Defining parameters

 Level: $$N$$ = $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$20$$ Sturm bound: $$127008$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(882))$$.

Total New Old
Modular forms 43296 10722 32574
Cusp forms 41376 10722 30654
Eisenstein series 1920 0 1920

## Trace form

 $$10722q + 8q^{4} - 6q^{5} - 12q^{6} - 8q^{7} + 12q^{9} + O(q^{10})$$ $$10722q + 8q^{4} - 6q^{5} - 12q^{6} - 8q^{7} + 12q^{9} - 36q^{10} - 18q^{11} + 12q^{12} - 106q^{13} - 108q^{14} - 222q^{15} - 48q^{16} - 372q^{17} - 120q^{18} - 196q^{19} - 36q^{20} + 36q^{21} + 84q^{22} + 390q^{23} + 96q^{24} + 570q^{25} + 528q^{26} + 504q^{27} + 84q^{28} + 786q^{29} + 312q^{30} - 94q^{31} - 330q^{33} + 60q^{34} - 390q^{35} + 12q^{36} - 816q^{37} - 468q^{38} - 246q^{39} - 264q^{40} - 714q^{41} - 338q^{43} - 240q^{44} + 330q^{45} - 300q^{46} + 486q^{47} + 24q^{48} + 312q^{49} + 936q^{50} + 2232q^{51} - 212q^{52} + 2808q^{53} + 1188q^{54} + 1506q^{55} + 288q^{56} + 1104q^{57} + 324q^{58} + 1566q^{59} + 252q^{60} + 1336q^{61} + 588q^{62} - 168q^{63} - 112q^{64} - 246q^{65} - 840q^{66} + 690q^{67} - 480q^{68} - 1998q^{69} + 396q^{70} - 1968q^{71} - 96q^{72} + 20q^{73} - 984q^{74} - 3708q^{75} + 584q^{76} - 954q^{77} - 1392q^{78} - 126q^{79} - 48q^{80} - 300q^{81} + 252q^{82} - 1554q^{83} - 744q^{85} - 1020q^{86} - 990q^{87} - 600q^{88} - 3228q^{89} - 1344q^{90} - 1328q^{91} - 876q^{92} - 1146q^{93} - 1572q^{94} - 1824q^{95} - 144q^{96} - 1426q^{97} - 744q^{98} - 66q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(882))$$

We only show spaces with odd 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
882.3.b $$\chi_{882}(197, \cdot)$$ 882.3.b.a 2 1
882.3.b.b 2
882.3.b.c 2
882.3.b.d 2
882.3.b.e 2
882.3.b.f 4
882.3.b.g 4
882.3.b.h 4
882.3.b.i 4
882.3.c $$\chi_{882}(685, \cdot)$$ 882.3.c.a 4 1
882.3.c.b 4
882.3.c.c 4
882.3.c.d 4
882.3.c.e 4
882.3.c.f 4
882.3.c.g 8
882.3.i $$\chi_{882}(569, \cdot)$$ n/a 160 2
882.3.j $$\chi_{882}(31, \cdot)$$ n/a 160 2
882.3.n $$\chi_{882}(19, \cdot)$$ 882.3.n.a 4 2
882.3.n.b 4
882.3.n.c 4
882.3.n.d 4
882.3.n.e 4
882.3.n.f 8
882.3.n.g 8
882.3.n.h 8
882.3.n.i 8
882.3.n.j 8
882.3.n.k 8
882.3.o $$\chi_{882}(97, \cdot)$$ n/a 160 2
882.3.p $$\chi_{882}(607, \cdot)$$ n/a 160 2
882.3.q $$\chi_{882}(491, \cdot)$$ n/a 164 2
882.3.r $$\chi_{882}(263, \cdot)$$ n/a 160 2
882.3.s $$\chi_{882}(557, \cdot)$$ 882.3.s.a 4 2
882.3.s.b 4
882.3.s.c 4
882.3.s.d 4
882.3.s.e 8
882.3.s.f 8
882.3.s.g 8
882.3.s.h 8
882.3.s.i 8
882.3.w $$\chi_{882}(55, \cdot)$$ n/a 288 6
882.3.x $$\chi_{882}(71, \cdot)$$ n/a 240 6
882.3.bd $$\chi_{882}(53, \cdot)$$ n/a 432 12
882.3.be $$\chi_{882}(11, \cdot)$$ n/a 1344 12
882.3.bf $$\chi_{882}(29, \cdot)$$ n/a 1344 12
882.3.bg $$\chi_{882}(103, \cdot)$$ n/a 1344 12
882.3.bh $$\chi_{882}(13, \cdot)$$ n/a 1344 12
882.3.bi $$\chi_{882}(73, \cdot)$$ n/a 552 12
882.3.bm $$\chi_{882}(61, \cdot)$$ n/a 1344 12
882.3.bn $$\chi_{882}(65, \cdot)$$ n/a 1344 12

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(882))$$ into lower level spaces

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