# Properties

 Label 1002.2 Level 1002 Weight 2 Dimension 6973 Nonzero newspaces 4 Sturm bound 111552 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1002 = 2 \cdot 3 \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Sturm bound: $$111552$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1002))$$.

Total New Old
Modular forms 28552 6973 21579
Cusp forms 27225 6973 20252
Eisenstein series 1327 0 1327

## Trace form

 $$6973q$$ $$\mathstrut +\mathstrut q^{2}$$ $$\mathstrut +\mathstrut q^{3}$$ $$\mathstrut +\mathstrut q^{4}$$ $$\mathstrut +\mathstrut 6q^{5}$$ $$\mathstrut +\mathstrut q^{6}$$ $$\mathstrut +\mathstrut 8q^{7}$$ $$\mathstrut +\mathstrut q^{8}$$ $$\mathstrut +\mathstrut q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$6973q$$ $$\mathstrut +\mathstrut q^{2}$$ $$\mathstrut +\mathstrut q^{3}$$ $$\mathstrut +\mathstrut q^{4}$$ $$\mathstrut +\mathstrut 6q^{5}$$ $$\mathstrut +\mathstrut q^{6}$$ $$\mathstrut +\mathstrut 8q^{7}$$ $$\mathstrut +\mathstrut q^{8}$$ $$\mathstrut +\mathstrut q^{9}$$ $$\mathstrut +\mathstrut 6q^{10}$$ $$\mathstrut +\mathstrut 12q^{11}$$ $$\mathstrut +\mathstrut q^{12}$$ $$\mathstrut +\mathstrut 14q^{13}$$ $$\mathstrut +\mathstrut 8q^{14}$$ $$\mathstrut +\mathstrut 6q^{15}$$ $$\mathstrut +\mathstrut q^{16}$$ $$\mathstrut +\mathstrut 18q^{17}$$ $$\mathstrut +\mathstrut q^{18}$$ $$\mathstrut +\mathstrut 20q^{19}$$ $$\mathstrut +\mathstrut 6q^{20}$$ $$\mathstrut +\mathstrut 8q^{21}$$ $$\mathstrut +\mathstrut 12q^{22}$$ $$\mathstrut +\mathstrut 24q^{23}$$ $$\mathstrut +\mathstrut q^{24}$$ $$\mathstrut +\mathstrut 31q^{25}$$ $$\mathstrut +\mathstrut 14q^{26}$$ $$\mathstrut +\mathstrut q^{27}$$ $$\mathstrut +\mathstrut 8q^{28}$$ $$\mathstrut +\mathstrut 30q^{29}$$ $$\mathstrut +\mathstrut 6q^{30}$$ $$\mathstrut +\mathstrut 32q^{31}$$ $$\mathstrut +\mathstrut q^{32}$$ $$\mathstrut +\mathstrut 12q^{33}$$ $$\mathstrut +\mathstrut 18q^{34}$$ $$\mathstrut +\mathstrut 48q^{35}$$ $$\mathstrut +\mathstrut q^{36}$$ $$\mathstrut +\mathstrut 38q^{37}$$ $$\mathstrut +\mathstrut 20q^{38}$$ $$\mathstrut +\mathstrut 14q^{39}$$ $$\mathstrut +\mathstrut 6q^{40}$$ $$\mathstrut +\mathstrut 42q^{41}$$ $$\mathstrut +\mathstrut 8q^{42}$$ $$\mathstrut +\mathstrut 44q^{43}$$ $$\mathstrut +\mathstrut 12q^{44}$$ $$\mathstrut +\mathstrut 6q^{45}$$ $$\mathstrut +\mathstrut 24q^{46}$$ $$\mathstrut +\mathstrut 48q^{47}$$ $$\mathstrut +\mathstrut q^{48}$$ $$\mathstrut +\mathstrut 57q^{49}$$ $$\mathstrut +\mathstrut 31q^{50}$$ $$\mathstrut +\mathstrut 18q^{51}$$ $$\mathstrut +\mathstrut 14q^{52}$$ $$\mathstrut +\mathstrut 54q^{53}$$ $$\mathstrut +\mathstrut q^{54}$$ $$\mathstrut +\mathstrut 72q^{55}$$ $$\mathstrut +\mathstrut 8q^{56}$$ $$\mathstrut +\mathstrut 20q^{57}$$ $$\mathstrut +\mathstrut 30q^{58}$$ $$\mathstrut +\mathstrut 60q^{59}$$ $$\mathstrut +\mathstrut 6q^{60}$$ $$\mathstrut +\mathstrut 62q^{61}$$ $$\mathstrut +\mathstrut 32q^{62}$$ $$\mathstrut +\mathstrut 8q^{63}$$ $$\mathstrut +\mathstrut q^{64}$$ $$\mathstrut +\mathstrut 84q^{65}$$ $$\mathstrut +\mathstrut 12q^{66}$$ $$\mathstrut +\mathstrut 68q^{67}$$ $$\mathstrut +\mathstrut 18q^{68}$$ $$\mathstrut +\mathstrut 24q^{69}$$ $$\mathstrut +\mathstrut 48q^{70}$$ $$\mathstrut +\mathstrut 72q^{71}$$ $$\mathstrut +\mathstrut q^{72}$$ $$\mathstrut +\mathstrut 74q^{73}$$ $$\mathstrut +\mathstrut 38q^{74}$$ $$\mathstrut +\mathstrut 31q^{75}$$ $$\mathstrut +\mathstrut 20q^{76}$$ $$\mathstrut +\mathstrut 96q^{77}$$ $$\mathstrut +\mathstrut 14q^{78}$$ $$\mathstrut +\mathstrut 80q^{79}$$ $$\mathstrut +\mathstrut 6q^{80}$$ $$\mathstrut +\mathstrut q^{81}$$ $$\mathstrut +\mathstrut 42q^{82}$$ $$\mathstrut +\mathstrut 84q^{83}$$ $$\mathstrut +\mathstrut 8q^{84}$$ $$\mathstrut +\mathstrut 108q^{85}$$ $$\mathstrut +\mathstrut 44q^{86}$$ $$\mathstrut +\mathstrut 30q^{87}$$ $$\mathstrut +\mathstrut 12q^{88}$$ $$\mathstrut +\mathstrut 90q^{89}$$ $$\mathstrut +\mathstrut 6q^{90}$$ $$\mathstrut +\mathstrut 112q^{91}$$ $$\mathstrut +\mathstrut 24q^{92}$$ $$\mathstrut +\mathstrut 32q^{93}$$ $$\mathstrut +\mathstrut 48q^{94}$$ $$\mathstrut +\mathstrut 120q^{95}$$ $$\mathstrut +\mathstrut q^{96}$$ $$\mathstrut +\mathstrut 98q^{97}$$ $$\mathstrut +\mathstrut 57q^{98}$$ $$\mathstrut +\mathstrut 12q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1002))$$

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
1002.2.a $$\chi_{1002}(1, \cdot)$$ 1002.2.a.a 1 1
1002.2.a.b 1
1002.2.a.c 1
1002.2.a.d 1
1002.2.a.e 1
1002.2.a.f 2
1002.2.a.g 3
1002.2.a.h 3
1002.2.a.i 4
1002.2.a.j 5
1002.2.a.k 7
1002.2.d $$\chi_{1002}(1001, \cdot)$$ 1002.2.d.a 56 1
1002.2.e $$\chi_{1002}(7, \cdot)$$ n/a 2296 82
1002.2.f $$\chi_{1002}(5, \cdot)$$ n/a 4592 82

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1002))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1002)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(501))$$$$^{\oplus 2}$$