# Properties

 Label 145.2 Level 145 Weight 2 Dimension 685 Nonzero newspaces 12 Newform subspaces 22 Sturm bound 3360 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$145 = 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$22$$ Sturm bound: $$3360$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(145))$$.

Total New Old
Modular forms 952 849 103
Cusp forms 729 685 44
Eisenstein series 223 164 59

## Trace form

 $$685 q - 31 q^{2} - 32 q^{3} - 35 q^{4} - 43 q^{5} - 96 q^{6} - 36 q^{7} - 43 q^{8} - 41 q^{9} + O(q^{10})$$ $$685 q - 31 q^{2} - 32 q^{3} - 35 q^{4} - 43 q^{5} - 96 q^{6} - 36 q^{7} - 43 q^{8} - 41 q^{9} - 45 q^{10} - 96 q^{11} - 56 q^{12} - 42 q^{13} - 52 q^{14} - 46 q^{15} - 115 q^{16} - 46 q^{17} - 67 q^{18} - 48 q^{19} - 28 q^{20} - 60 q^{21} - 8 q^{22} - 24 q^{23} + 80 q^{24} - 15 q^{25} - 56 q^{26} + 16 q^{27} + 56 q^{28} - q^{29} - 12 q^{30} - 60 q^{31} + 21 q^{32} + 8 q^{33} - 12 q^{34} - 22 q^{35} - 7 q^{36} - 38 q^{37} - 32 q^{38} - 28 q^{39} - 36 q^{40} - 126 q^{41} - 124 q^{42} - 72 q^{43} - 84 q^{44} - 20 q^{45} - 16 q^{46} - 20 q^{47} + 72 q^{48} + 27 q^{49} + 53 q^{50} - 44 q^{51} + 98 q^{52} + 44 q^{53} + 104 q^{54} + 58 q^{55} + 48 q^{56} + 32 q^{57} + 221 q^{58} - 60 q^{59} + 126 q^{60} - 34 q^{61} + 72 q^{62} + 92 q^{63} + 97 q^{64} + 7 q^{65} - 4 q^{66} + 16 q^{67} + 42 q^{68} - 12 q^{69} + 74 q^{70} - 16 q^{71} + 85 q^{72} + 24 q^{73} + 54 q^{74} + 24 q^{75} + 16 q^{77} + 28 q^{78} - 52 q^{79} + 123 q^{80} + 19 q^{81} - 42 q^{82} + 168 q^{84} + 24 q^{85} + 92 q^{86} - 4 q^{87} + 100 q^{88} + 22 q^{89} + 101 q^{90} - 28 q^{91} + 140 q^{92} - 44 q^{93} - 60 q^{94} + 50 q^{95} + 140 q^{96} + 28 q^{97} + 165 q^{98} + 180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$

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
145.2.a $$\chi_{145}(1, \cdot)$$ 145.2.a.a 1 1
145.2.a.b 2
145.2.a.c 3
145.2.a.d 3
145.2.b $$\chi_{145}(59, \cdot)$$ 145.2.b.a 4 1
145.2.b.b 4
145.2.b.c 6
145.2.c $$\chi_{145}(86, \cdot)$$ 145.2.c.a 4 1
145.2.c.b 6
145.2.d $$\chi_{145}(144, \cdot)$$ 145.2.d.a 4 1
145.2.d.b 4
145.2.d.c 4
145.2.e $$\chi_{145}(12, \cdot)$$ 145.2.e.a 26 2
145.2.j $$\chi_{145}(17, \cdot)$$ 145.2.j.a 26 2
145.2.k $$\chi_{145}(16, \cdot)$$ 145.2.k.a 24 6
145.2.k.b 36
145.2.l $$\chi_{145}(4, \cdot)$$ 145.2.l.a 72 6
145.2.m $$\chi_{145}(6, \cdot)$$ 145.2.m.a 24 6
145.2.m.b 36
145.2.n $$\chi_{145}(24, \cdot)$$ 145.2.n.a 84 6
145.2.o $$\chi_{145}(2, \cdot)$$ 145.2.o.a 156 12
145.2.t $$\chi_{145}(3, \cdot)$$ 145.2.t.a 156 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(145))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(145)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 1}$$