## Defining parameters

 Level: $$N$$ = $$2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$912384$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2898))$$.

Total New Old
Modular forms 232320 57464 174856
Cusp forms 223873 57464 166409
Eisenstein series 8447 0 8447

## Trace form

 $$57464 q - 4 q^{2} - 12 q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} - 20 q^{7} + 8 q^{8} + 12 q^{9} + O(q^{10})$$ $$57464 q - 4 q^{2} - 12 q^{3} - 8 q^{4} - 12 q^{5} + 12 q^{6} - 20 q^{7} + 8 q^{8} + 12 q^{9} - 12 q^{10} - 12 q^{11} - 12 q^{13} + 32 q^{14} + 48 q^{15} + 8 q^{16} + 28 q^{17} + 24 q^{18} + 16 q^{19} - 8 q^{20} + 84 q^{21} + 40 q^{22} - 28 q^{23} + 12 q^{24} - 8 q^{25} + 32 q^{26} + 72 q^{27} - 14 q^{28} - 20 q^{29} + 24 q^{30} - 20 q^{31} - 4 q^{32} + 12 q^{33} - 12 q^{34} + 38 q^{35} + 12 q^{36} - 104 q^{37} - 32 q^{38} + 72 q^{39} - 12 q^{40} + 16 q^{41} - 92 q^{43} - 48 q^{44} + 96 q^{45} - 48 q^{46} + 8 q^{47} + 12 q^{48} - 10 q^{49} - 100 q^{50} - 36 q^{51} + 12 q^{52} - 92 q^{53} - 20 q^{54} + 176 q^{55} + 50 q^{56} + 84 q^{57} + 288 q^{58} + 244 q^{59} - 56 q^{60} + 540 q^{61} + 196 q^{62} - 140 q^{63} + 4 q^{64} + 588 q^{65} + 160 q^{66} + 316 q^{67} + 156 q^{68} + 332 q^{69} + 300 q^{70} + 420 q^{71} + 188 q^{72} + 312 q^{73} + 400 q^{74} + 388 q^{75} + 198 q^{77} + 144 q^{78} + 476 q^{79} + 120 q^{80} + 340 q^{81} + 264 q^{82} + 292 q^{83} + 32 q^{84} + 100 q^{85} + 112 q^{86} + 216 q^{87} + 36 q^{88} + 124 q^{89} + 96 q^{90} + 88 q^{91} + 36 q^{92} + 216 q^{93} + 96 q^{94} + 156 q^{95} + 24 q^{96} - 68 q^{97} + 108 q^{98} + 312 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2898))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2898.2.a $$\chi_{2898}(1, \cdot)$$ 2898.2.a.a 1 1
2898.2.a.b 1
2898.2.a.c 1
2898.2.a.d 1
2898.2.a.e 1
2898.2.a.f 1
2898.2.a.g 1
2898.2.a.h 1
2898.2.a.i 1
2898.2.a.j 1
2898.2.a.k 1
2898.2.a.l 1
2898.2.a.m 1
2898.2.a.n 1
2898.2.a.o 1
2898.2.a.p 1
2898.2.a.q 1
2898.2.a.r 1
2898.2.a.s 1
2898.2.a.t 1
2898.2.a.u 1
2898.2.a.v 2
2898.2.a.w 2
2898.2.a.x 2
2898.2.a.y 2
2898.2.a.z 2
2898.2.a.ba 2
2898.2.a.bb 2
2898.2.a.bc 2
2898.2.a.bd 2
2898.2.a.be 3
2898.2.a.bf 3
2898.2.a.bg 3
2898.2.a.bh 4
2898.2.a.bi 4
2898.2.f $$\chi_{2898}(2393, \cdot)$$ 2898.2.f.a 32 1
2898.2.f.b 32
2898.2.g $$\chi_{2898}(2575, \cdot)$$ 2898.2.g.a 4 1
2898.2.g.b 4
2898.2.g.c 4
2898.2.g.d 4
2898.2.g.e 4
2898.2.g.f 4
2898.2.g.g 4
2898.2.g.h 4
2898.2.g.i 16
2898.2.g.j 16
2898.2.g.k 16
2898.2.h $$\chi_{2898}(827, \cdot)$$ 2898.2.h.a 24 1
2898.2.h.b 24
2898.2.i $$\chi_{2898}(277, \cdot)$$ n/a 352 2
2898.2.j $$\chi_{2898}(967, \cdot)$$ n/a 264 2
2898.2.k $$\chi_{2898}(415, \cdot)$$ n/a 144 2
2898.2.l $$\chi_{2898}(2209, \cdot)$$ n/a 352 2
2898.2.q $$\chi_{2898}(137, \cdot)$$ n/a 384 2
2898.2.r $$\chi_{2898}(1793, \cdot)$$ n/a 288 2
2898.2.s $$\chi_{2898}(1241, \cdot)$$ n/a 128 2
2898.2.t $$\chi_{2898}(1333, \cdot)$$ n/a 160 2
2898.2.u $$\chi_{2898}(1151, \cdot)$$ n/a 112 2
2898.2.v $$\chi_{2898}(229, \cdot)$$ n/a 384 2
2898.2.w $$\chi_{2898}(1013, \cdot)$$ n/a 352 2
2898.2.x $$\chi_{2898}(461, \cdot)$$ n/a 352 2
2898.2.y $$\chi_{2898}(643, \cdot)$$ n/a 384 2
2898.2.bl $$\chi_{2898}(1195, \cdot)$$ n/a 384 2
2898.2.bm $$\chi_{2898}(47, \cdot)$$ n/a 352 2
2898.2.bn $$\chi_{2898}(1103, \cdot)$$ n/a 384 2
2898.2.bo $$\chi_{2898}(127, \cdot)$$ n/a 600 10
2898.2.bp $$\chi_{2898}(701, \cdot)$$ n/a 480 10
2898.2.bq $$\chi_{2898}(181, \cdot)$$ n/a 800 10
2898.2.br $$\chi_{2898}(377, \cdot)$$ n/a 640 10
2898.2.bw $$\chi_{2898}(193, \cdot)$$ n/a 3840 20
2898.2.bx $$\chi_{2898}(163, \cdot)$$ n/a 1600 20
2898.2.by $$\chi_{2898}(85, \cdot)$$ n/a 2880 20
2898.2.bz $$\chi_{2898}(25, \cdot)$$ n/a 3840 20
2898.2.ca $$\chi_{2898}(65, \cdot)$$ n/a 3840 20
2898.2.cb $$\chi_{2898}(59, \cdot)$$ n/a 3840 20
2898.2.cc $$\chi_{2898}(61, \cdot)$$ n/a 3840 20
2898.2.cp $$\chi_{2898}(97, \cdot)$$ n/a 3840 20
2898.2.cq $$\chi_{2898}(41, \cdot)$$ n/a 3840 20
2898.2.cr $$\chi_{2898}(101, \cdot)$$ n/a 3840 20
2898.2.cs $$\chi_{2898}(103, \cdot)$$ n/a 3840 20
2898.2.ct $$\chi_{2898}(215, \cdot)$$ n/a 1280 20
2898.2.cu $$\chi_{2898}(19, \cdot)$$ n/a 1600 20
2898.2.cv $$\chi_{2898}(53, \cdot)$$ n/a 1280 20
2898.2.cw $$\chi_{2898}(113, \cdot)$$ n/a 2880 20
2898.2.cx $$\chi_{2898}(11, \cdot)$$ n/a 3840 20

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2898))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2898)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(126))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(414))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(966))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1449))$$$$^{\oplus 2}$$