# Properties

 Label 130.2 Level 130 Weight 2 Dimension 155 Nonzero newspaces 12 Newforms 30 Sturm bound 2016 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$130 = 2 \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$30$$ Sturm bound: $$2016$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(130))$$.

Total New Old
Modular forms 600 155 445
Cusp forms 409 155 254
Eisenstein series 191 0 191

## Trace form

 $$155q$$ $$\mathstrut +\mathstrut q^{2}$$ $$\mathstrut +\mathstrut 4q^{3}$$ $$\mathstrut +\mathstrut q^{4}$$ $$\mathstrut +\mathstrut q^{5}$$ $$\mathstrut +\mathstrut 4q^{6}$$ $$\mathstrut -\mathstrut 5q^{8}$$ $$\mathstrut -\mathstrut 19q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$155q$$ $$\mathstrut +\mathstrut q^{2}$$ $$\mathstrut +\mathstrut 4q^{3}$$ $$\mathstrut +\mathstrut q^{4}$$ $$\mathstrut +\mathstrut q^{5}$$ $$\mathstrut +\mathstrut 4q^{6}$$ $$\mathstrut -\mathstrut 5q^{8}$$ $$\mathstrut -\mathstrut 19q^{9}$$ $$\mathstrut -\mathstrut 14q^{10}$$ $$\mathstrut -\mathstrut 12q^{11}$$ $$\mathstrut -\mathstrut 4q^{12}$$ $$\mathstrut -\mathstrut 35q^{13}$$ $$\mathstrut -\mathstrut 16q^{14}$$ $$\mathstrut -\mathstrut 20q^{15}$$ $$\mathstrut -\mathstrut 7q^{16}$$ $$\mathstrut -\mathstrut 12q^{17}$$ $$\mathstrut -\mathstrut 17q^{18}$$ $$\mathstrut -\mathstrut 36q^{19}$$ $$\mathstrut -\mathstrut 2q^{20}$$ $$\mathstrut -\mathstrut 24q^{21}$$ $$\mathstrut +\mathstrut 12q^{22}$$ $$\mathstrut +\mathstrut 4q^{24}$$ $$\mathstrut +\mathstrut q^{25}$$ $$\mathstrut +\mathstrut 13q^{26}$$ $$\mathstrut -\mathstrut 32q^{27}$$ $$\mathstrut -\mathstrut 48q^{29}$$ $$\mathstrut -\mathstrut 20q^{30}$$ $$\mathstrut -\mathstrut 48q^{31}$$ $$\mathstrut +\mathstrut q^{32}$$ $$\mathstrut -\mathstrut 72q^{33}$$ $$\mathstrut -\mathstrut 30q^{34}$$ $$\mathstrut -\mathstrut 64q^{35}$$ $$\mathstrut -\mathstrut 35q^{36}$$ $$\mathstrut -\mathstrut 24q^{37}$$ $$\mathstrut -\mathstrut 52q^{38}$$ $$\mathstrut -\mathstrut 52q^{39}$$ $$\mathstrut +\mathstrut q^{40}$$ $$\mathstrut -\mathstrut 60q^{41}$$ $$\mathstrut -\mathstrut 40q^{42}$$ $$\mathstrut -\mathstrut 44q^{43}$$ $$\mathstrut -\mathstrut 36q^{44}$$ $$\mathstrut -\mathstrut 62q^{45}$$ $$\mathstrut -\mathstrut 24q^{46}$$ $$\mathstrut -\mathstrut 48q^{47}$$ $$\mathstrut +\mathstrut 4q^{48}$$ $$\mathstrut -\mathstrut 7q^{49}$$ $$\mathstrut -\mathstrut 14q^{50}$$ $$\mathstrut +\mathstrut 24q^{51}$$ $$\mathstrut +\mathstrut 11q^{52}$$ $$\mathstrut +\mathstrut 78q^{53}$$ $$\mathstrut +\mathstrut 112q^{54}$$ $$\mathstrut +\mathstrut 96q^{55}$$ $$\mathstrut +\mathstrut 32q^{56}$$ $$\mathstrut +\mathstrut 192q^{57}$$ $$\mathstrut +\mathstrut 84q^{58}$$ $$\mathstrut +\mathstrut 108q^{59}$$ $$\mathstrut +\mathstrut 76q^{60}$$ $$\mathstrut +\mathstrut 80q^{61}$$ $$\mathstrut +\mathstrut 104q^{62}$$ $$\mathstrut +\mathstrut 192q^{63}$$ $$\mathstrut +\mathstrut 7q^{64}$$ $$\mathstrut +\mathstrut 118q^{65}$$ $$\mathstrut +\mathstrut 144q^{66}$$ $$\mathstrut +\mathstrut 108q^{67}$$ $$\mathstrut +\mathstrut 24q^{68}$$ $$\mathstrut +\mathstrut 192q^{69}$$ $$\mathstrut +\mathstrut 116q^{70}$$ $$\mathstrut +\mathstrut 24q^{71}$$ $$\mathstrut +\mathstrut 61q^{72}$$ $$\mathstrut +\mathstrut 42q^{73}$$ $$\mathstrut +\mathstrut 68q^{74}$$ $$\mathstrut +\mathstrut 116q^{75}$$ $$\mathstrut +\mathstrut 12q^{76}$$ $$\mathstrut +\mathstrut 76q^{78}$$ $$\mathstrut -\mathstrut 16q^{79}$$ $$\mathstrut +\mathstrut 10q^{80}$$ $$\mathstrut -\mathstrut 31q^{81}$$ $$\mathstrut -\mathstrut 48q^{82}$$ $$\mathstrut -\mathstrut 108q^{83}$$ $$\mathstrut -\mathstrut 24q^{84}$$ $$\mathstrut -\mathstrut 105q^{85}$$ $$\mathstrut -\mathstrut 4q^{86}$$ $$\mathstrut -\mathstrut 120q^{87}$$ $$\mathstrut +\mathstrut 12q^{88}$$ $$\mathstrut -\mathstrut 102q^{89}$$ $$\mathstrut -\mathstrut 47q^{90}$$ $$\mathstrut -\mathstrut 48q^{91}$$ $$\mathstrut -\mathstrut 24q^{92}$$ $$\mathstrut -\mathstrut 96q^{93}$$ $$\mathstrut -\mathstrut 72q^{94}$$ $$\mathstrut -\mathstrut 52q^{95}$$ $$\mathstrut +\mathstrut 4q^{96}$$ $$\mathstrut -\mathstrut 102q^{97}$$ $$\mathstrut -\mathstrut 39q^{98}$$ $$\mathstrut -\mathstrut 60q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$

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
130.2.a $$\chi_{130}(1, \cdot)$$ 130.2.a.a 1 1
130.2.a.b 1
130.2.a.c 1
130.2.b $$\chi_{130}(79, \cdot)$$ 130.2.b.a 6 1
130.2.c $$\chi_{130}(129, \cdot)$$ 130.2.c.a 4 1
130.2.c.b 4
130.2.d $$\chi_{130}(51, \cdot)$$ 130.2.d.a 2 1
130.2.e $$\chi_{130}(61, \cdot)$$ 130.2.e.a 2 2
130.2.e.b 2
130.2.e.c 4
130.2.e.d 4
130.2.g $$\chi_{130}(57, \cdot)$$ 130.2.g.a 2 2
130.2.g.b 2
130.2.g.c 2
130.2.g.d 4
130.2.g.e 4
130.2.j $$\chi_{130}(47, \cdot)$$ 130.2.j.a 2 2
130.2.j.b 2
130.2.j.c 2
130.2.j.d 4
130.2.j.e 4
130.2.l $$\chi_{130}(101, \cdot)$$ 130.2.l.a 4 2
130.2.l.b 8
130.2.m $$\chi_{130}(49, \cdot)$$ 130.2.m.a 8 2
130.2.m.b 8
130.2.n $$\chi_{130}(9, \cdot)$$ 130.2.n.a 12 2
130.2.p $$\chi_{130}(7, \cdot)$$ 130.2.p.a 12 4
130.2.p.b 16
130.2.s $$\chi_{130}(33, \cdot)$$ 130.2.s.a 12 4
130.2.s.b 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(130))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(130)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 2}$$