# Properties

 Label 592.2 Level 592 Weight 2 Dimension 5990 Nonzero newspaces 21 Newform subspaces 68 Sturm bound 43776 Trace bound 7

## Defining parameters

 Level: $$N$$ = $$592 = 2^{4} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$21$$ Newform subspaces: $$68$$ Sturm bound: $$43776$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(592))$$.

Total New Old
Modular forms 11448 6304 5144
Cusp forms 10441 5990 4451
Eisenstein series 1007 314 693

## Trace form

 $$5990 q - 68 q^{2} - 50 q^{3} - 72 q^{4} - 86 q^{5} - 80 q^{6} - 54 q^{7} - 80 q^{8} - 18 q^{9} + O(q^{10})$$ $$5990 q - 68 q^{2} - 50 q^{3} - 72 q^{4} - 86 q^{5} - 80 q^{6} - 54 q^{7} - 80 q^{8} - 18 q^{9} - 72 q^{10} - 58 q^{11} - 64 q^{12} - 86 q^{13} - 64 q^{14} - 62 q^{15} - 56 q^{16} - 154 q^{17} - 76 q^{18} - 66 q^{19} - 80 q^{20} - 98 q^{21} - 72 q^{22} - 54 q^{23} - 72 q^{24} - 18 q^{25} - 80 q^{26} - 38 q^{27} - 88 q^{28} - 102 q^{29} - 64 q^{30} - 22 q^{31} - 88 q^{32} - 154 q^{33} - 80 q^{34} - 46 q^{35} - 64 q^{36} - 96 q^{37} - 120 q^{38} - 54 q^{39} - 56 q^{40} - 18 q^{41} - 72 q^{42} - 74 q^{43} - 64 q^{44} - 94 q^{45} - 96 q^{46} - 86 q^{47} - 88 q^{48} - 174 q^{49} - 60 q^{50} - 62 q^{51} - 64 q^{52} - 70 q^{53} - 72 q^{54} - 54 q^{55} - 56 q^{56} - 18 q^{57} - 48 q^{58} - 42 q^{59} - 72 q^{60} - 54 q^{61} - 104 q^{62} - 62 q^{63} - 72 q^{64} - 170 q^{65} - 80 q^{66} - 34 q^{67} - 72 q^{68} - 66 q^{69} - 88 q^{70} - 54 q^{71} - 80 q^{72} - 36 q^{73} - 72 q^{74} - 120 q^{75} - 96 q^{76} - 98 q^{77} - 64 q^{78} - 54 q^{79} - 88 q^{80} - 182 q^{81} - 72 q^{82} - 50 q^{83} - 56 q^{84} - 98 q^{85} - 72 q^{86} - 54 q^{87} - 88 q^{88} - 18 q^{89} - 64 q^{90} - 62 q^{91} - 24 q^{92} - 122 q^{93} - 40 q^{94} - 30 q^{95} - 40 q^{96} - 154 q^{97} - 60 q^{98} - 50 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(592))$$

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
592.2.a $$\chi_{592}(1, \cdot)$$ 592.2.a.a 1 1
592.2.a.b 1
592.2.a.c 1
592.2.a.d 1
592.2.a.e 1
592.2.a.f 2
592.2.a.g 2
592.2.a.h 2
592.2.a.i 3
592.2.a.j 4
592.2.c $$\chi_{592}(297, \cdot)$$ None 0 1
592.2.e $$\chi_{592}(73, \cdot)$$ None 0 1
592.2.g $$\chi_{592}(369, \cdot)$$ 592.2.g.a 2 1
592.2.g.b 2
592.2.g.c 4
592.2.g.d 10
592.2.i $$\chi_{592}(417, \cdot)$$ 592.2.i.a 2 2
592.2.i.b 2
592.2.i.c 2
592.2.i.d 2
592.2.i.e 6
592.2.i.f 6
592.2.i.g 6
592.2.i.h 10
592.2.j $$\chi_{592}(327, \cdot)$$ None 0 2
592.2.m $$\chi_{592}(43, \cdot)$$ 592.2.m.a 148 2
592.2.n $$\chi_{592}(221, \cdot)$$ 592.2.n.a 148 2
592.2.o $$\chi_{592}(149, \cdot)$$ 592.2.o.a 144 2
592.2.s $$\chi_{592}(339, \cdot)$$ 592.2.s.a 148 2
592.2.t $$\chi_{592}(31, \cdot)$$ 592.2.t.a 2 2
592.2.t.b 4
592.2.t.c 4
592.2.t.d 28
592.2.w $$\chi_{592}(529, \cdot)$$ 592.2.w.a 2 2
592.2.w.b 2
592.2.w.c 4
592.2.w.d 4
592.2.w.e 4
592.2.w.f 20
592.2.y $$\chi_{592}(233, \cdot)$$ None 0 2
592.2.ba $$\chi_{592}(121, \cdot)$$ None 0 2
592.2.bc $$\chi_{592}(33, \cdot)$$ 592.2.bc.a 6 6
592.2.bc.b 6
592.2.bc.c 6
592.2.bc.d 12
592.2.bc.e 24
592.2.bc.f 24
592.2.bc.g 30
592.2.be $$\chi_{592}(319, \cdot)$$ 592.2.be.a 4 4
592.2.be.b 8
592.2.be.c 8
592.2.be.d 16
592.2.be.e 20
592.2.be.f 20
592.2.bf $$\chi_{592}(251, \cdot)$$ 592.2.bf.a 296 4
592.2.bj $$\chi_{592}(269, \cdot)$$ 592.2.bj.a 296 4
592.2.bk $$\chi_{592}(85, \cdot)$$ 592.2.bk.a 296 4
592.2.bl $$\chi_{592}(51, \cdot)$$ 592.2.bl.a 296 4
592.2.bo $$\chi_{592}(23, \cdot)$$ None 0 4
592.2.bq $$\chi_{592}(65, \cdot)$$ 592.2.bq.a 6 6
592.2.bq.b 12
592.2.bq.c 12
592.2.bq.d 18
592.2.bq.e 60
592.2.bs $$\chi_{592}(9, \cdot)$$ None 0 6
592.2.bv $$\chi_{592}(25, \cdot)$$ None 0 6
592.2.bx $$\chi_{592}(15, \cdot)$$ 592.2.bx.a 12 12
592.2.bx.b 12
592.2.bx.c 12
592.2.bx.d 60
592.2.bx.e 60
592.2.bx.f 72
592.2.by $$\chi_{592}(21, \cdot)$$ 592.2.by.a 888 12
592.2.ca $$\chi_{592}(19, \cdot)$$ 592.2.ca.a 888 12
592.2.cd $$\chi_{592}(59, \cdot)$$ 592.2.cd.a 888 12
592.2.ce $$\chi_{592}(53, \cdot)$$ 592.2.ce.a 888 12
592.2.ch $$\chi_{592}(39, \cdot)$$ None 0 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(592))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(592)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(296))$$$$^{\oplus 2}$$