# Properties

 Label 798.2 Level 798 Weight 2 Dimension 4113 Nonzero newspaces 32 Newform subspaces 133 Sturm bound 69120 Trace bound 18

## Defining parameters

 Level: $$N$$ = $$798 = 2 \cdot 3 \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Newform subspaces: $$133$$ Sturm bound: $$69120$$ Trace bound: $$18$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(798))$$.

Total New Old
Modular forms 18144 4113 14031
Cusp forms 16417 4113 12304
Eisenstein series 1727 0 1727

## Trace form

 $$4113 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + O(q^{10})$$ $$4113 q - 3 q^{2} + q^{3} + 5 q^{4} + 6 q^{5} + 9 q^{6} + 17 q^{7} - 3 q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + 13 q^{12} + 86 q^{13} + 21 q^{14} + 54 q^{15} - 3 q^{16} + 42 q^{17} - 27 q^{18} + 145 q^{19} + 54 q^{20} + 7 q^{21} + 72 q^{22} + 24 q^{23} - 15 q^{24} + 99 q^{25} + 54 q^{26} + 31 q^{27} + 21 q^{28} + 30 q^{29} + 6 q^{30} + 56 q^{31} - 3 q^{32} + 120 q^{33} - 6 q^{34} + 78 q^{35} + 13 q^{36} + 70 q^{37} - 3 q^{38} + 122 q^{39} + 6 q^{40} + 42 q^{41} + 45 q^{42} + 172 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} - 17 q^{48} + 33 q^{49} + 3 q^{50} - 240 q^{51} - 58 q^{52} - 90 q^{53} - 147 q^{54} - 144 q^{55} + 9 q^{56} - 191 q^{57} - 114 q^{58} - 84 q^{59} - 114 q^{60} - 82 q^{61} - 48 q^{62} - 113 q^{63} + 5 q^{64} - 12 q^{65} - 180 q^{66} - 12 q^{67} - 30 q^{68} - 132 q^{69} - 90 q^{70} + 3 q^{72} - 10 q^{73} - 42 q^{74} + 67 q^{75} - 23 q^{76} + 108 q^{77} + 78 q^{78} + 312 q^{79} + 6 q^{80} + 253 q^{81} + 162 q^{82} + 276 q^{83} + 91 q^{84} + 348 q^{85} + 132 q^{86} + 390 q^{87} - 12 q^{88} + 210 q^{89} + 186 q^{90} + 206 q^{91} + 120 q^{92} + 260 q^{93} + 288 q^{94} + 90 q^{95} - 15 q^{96} + 122 q^{97} + 93 q^{98} + 126 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(798))$$

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
798.2.a $$\chi_{798}(1, \cdot)$$ 798.2.a.a 1 1
798.2.a.b 1
798.2.a.c 1
798.2.a.d 1
798.2.a.e 1
798.2.a.f 1
798.2.a.g 1
798.2.a.h 1
798.2.a.i 1
798.2.a.j 2
798.2.a.k 2
798.2.a.l 2
798.2.a.m 2
798.2.b $$\chi_{798}(113, \cdot)$$ 798.2.b.a 2 1
798.2.b.b 2
798.2.b.c 2
798.2.b.d 2
798.2.b.e 8
798.2.b.f 8
798.2.b.g 8
798.2.b.h 8
798.2.e $$\chi_{798}(265, \cdot)$$ 798.2.e.a 12 1
798.2.e.b 12
798.2.f $$\chi_{798}(419, \cdot)$$ 798.2.f.a 24 1
798.2.f.b 24
798.2.i $$\chi_{798}(163, \cdot)$$ 798.2.i.a 14 2
798.2.i.b 14
798.2.i.c 14
798.2.i.d 14
798.2.j $$\chi_{798}(457, \cdot)$$ 798.2.j.a 2 2
798.2.j.b 2
798.2.j.c 2
798.2.j.d 2
798.2.j.e 2
798.2.j.f 2
798.2.j.g 4
798.2.j.h 4
798.2.j.i 6
798.2.j.j 6
798.2.j.k 8
798.2.j.l 8
798.2.k $$\chi_{798}(463, \cdot)$$ 798.2.k.a 2 2
798.2.k.b 2
798.2.k.c 2
798.2.k.d 2
798.2.k.e 2
798.2.k.f 2
798.2.k.g 2
798.2.k.h 2
798.2.k.i 2
798.2.k.j 4
798.2.k.k 4
798.2.k.l 4
798.2.k.m 4
798.2.k.n 6
798.2.l $$\chi_{798}(121, \cdot)$$ 798.2.l.a 14 2
798.2.l.b 14
798.2.l.c 14
798.2.l.d 14
798.2.m $$\chi_{798}(145, \cdot)$$ 798.2.m.a 28 2
798.2.m.b 28
798.2.p $$\chi_{798}(107, \cdot)$$ 798.2.p.a 2 2
798.2.p.b 2
798.2.p.c 50
798.2.p.d 50
798.2.r $$\chi_{798}(83, \cdot)$$ 798.2.r.a 112 2
798.2.u $$\chi_{798}(647, \cdot)$$ 798.2.u.a 48 2
798.2.u.b 48
798.2.w $$\chi_{798}(311, \cdot)$$ 798.2.w.a 104 2
798.2.ba $$\chi_{798}(407, \cdot)$$ 798.2.ba.a 2 2
798.2.ba.b 2
798.2.ba.c 2
798.2.ba.d 2
798.2.ba.e 2
798.2.ba.f 2
798.2.ba.g 4
798.2.ba.h 4
798.2.ba.i 4
798.2.ba.j 4
798.2.ba.k 12
798.2.ba.l 12
798.2.ba.m 14
798.2.ba.n 14
798.2.bc $$\chi_{798}(31, \cdot)$$ 798.2.bc.a 28 2
798.2.bc.b 28
798.2.be $$\chi_{798}(493, \cdot)$$ 798.2.be.a 28 2
798.2.be.b 28
798.2.bf $$\chi_{798}(569, \cdot)$$ 798.2.bf.a 52 2
798.2.bf.b 52
798.2.bh $$\chi_{798}(65, \cdot)$$ 798.2.bh.a 2 2
798.2.bh.b 2
798.2.bh.c 50
798.2.bh.d 50
798.2.bj $$\chi_{798}(559, \cdot)$$ 798.2.bj.a 24 2
798.2.bj.b 24
798.2.bn $$\chi_{798}(353, \cdot)$$ 798.2.bn.a 104 2
798.2.bo $$\chi_{798}(43, \cdot)$$ 798.2.bo.a 12 6
798.2.bo.b 12
798.2.bo.c 12
798.2.bo.d 12
798.2.bo.e 18
798.2.bo.f 18
798.2.bo.g 18
798.2.bo.h 18
798.2.bp $$\chi_{798}(289, \cdot)$$ 798.2.bp.a 12 6
798.2.bp.b 12
798.2.bp.c 12
798.2.bp.d 36
798.2.bp.e 42
798.2.bp.f 42
798.2.bq $$\chi_{798}(25, \cdot)$$ 798.2.bq.a 12 6
798.2.bq.b 12
798.2.bq.c 12
798.2.bq.d 36
798.2.bq.e 42
798.2.bq.f 42
798.2.bt $$\chi_{798}(5, \cdot)$$ 798.2.bt.a 324 6
798.2.bu $$\chi_{798}(53, \cdot)$$ 798.2.bu.a 162 6
798.2.bu.b 162
798.2.bx $$\chi_{798}(13, \cdot)$$ 798.2.bx.a 84 6
798.2.bx.b 84
798.2.ca $$\chi_{798}(325, \cdot)$$ 798.2.ca.a 72 6
798.2.ca.b 84
798.2.cb $$\chi_{798}(17, \cdot)$$ 798.2.cb.a 324 6
798.2.cc $$\chi_{798}(317, \cdot)$$ 798.2.cc.a 162 6
798.2.cc.b 162
798.2.cf $$\chi_{798}(29, \cdot)$$ 798.2.cf.a 60 6
798.2.cf.b 60
798.2.cf.c 60
798.2.cf.d 60
798.2.cg $$\chi_{798}(251, \cdot)$$ 798.2.cg.a 312 6
798.2.cj $$\chi_{798}(241, \cdot)$$ 798.2.cj.a 72 6
798.2.cj.b 84

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(798))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(798)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(399))$$$$^{\oplus 2}$$