# Properties

 Label 1003.2 Level 1003 Weight 2 Dimension 40589 Nonzero newspaces 10 Sturm bound 167040 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1003 = 17 \cdot 59$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Sturm bound: $$167040$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1003))$$.

Total New Old
Modular forms 42688 42301 387
Cusp forms 40833 40589 244
Eisenstein series 1855 1712 143

## Trace form

 $$40589q$$ $$\mathstrut -\mathstrut 399q^{2}$$ $$\mathstrut -\mathstrut 402q^{3}$$ $$\mathstrut -\mathstrut 411q^{4}$$ $$\mathstrut -\mathstrut 408q^{5}$$ $$\mathstrut -\mathstrut 426q^{6}$$ $$\mathstrut -\mathstrut 414q^{7}$$ $$\mathstrut -\mathstrut 435q^{8}$$ $$\mathstrut -\mathstrut 429q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$40589q$$ $$\mathstrut -\mathstrut 399q^{2}$$ $$\mathstrut -\mathstrut 402q^{3}$$ $$\mathstrut -\mathstrut 411q^{4}$$ $$\mathstrut -\mathstrut 408q^{5}$$ $$\mathstrut -\mathstrut 426q^{6}$$ $$\mathstrut -\mathstrut 414q^{7}$$ $$\mathstrut -\mathstrut 435q^{8}$$ $$\mathstrut -\mathstrut 429q^{9}$$ $$\mathstrut -\mathstrut 436q^{10}$$ $$\mathstrut -\mathstrut 410q^{11}$$ $$\mathstrut -\mathstrut 426q^{12}$$ $$\mathstrut -\mathstrut 416q^{13}$$ $$\mathstrut -\mathstrut 430q^{14}$$ $$\mathstrut -\mathstrut 414q^{15}$$ $$\mathstrut -\mathstrut 411q^{16}$$ $$\mathstrut -\mathstrut 438q^{17}$$ $$\mathstrut -\mathstrut 891q^{18}$$ $$\mathstrut -\mathstrut 434q^{19}$$ $$\mathstrut -\mathstrut 460q^{20}$$ $$\mathstrut -\mathstrut 438q^{21}$$ $$\mathstrut -\mathstrut 466q^{22}$$ $$\mathstrut -\mathstrut 446q^{23}$$ $$\mathstrut -\mathstrut 490q^{24}$$ $$\mathstrut -\mathstrut 427q^{25}$$ $$\mathstrut -\mathstrut 444q^{26}$$ $$\mathstrut -\mathstrut 462q^{27}$$ $$\mathstrut -\mathstrut 462q^{28}$$ $$\mathstrut -\mathstrut 440q^{29}$$ $$\mathstrut -\mathstrut 478q^{30}$$ $$\mathstrut -\mathstrut 422q^{31}$$ $$\mathstrut -\mathstrut 467q^{32}$$ $$\mathstrut -\mathstrut 454q^{33}$$ $$\mathstrut -\mathstrut 396q^{34}$$ $$\mathstrut -\mathstrut 918q^{35}$$ $$\mathstrut -\mathstrut 503q^{36}$$ $$\mathstrut -\mathstrut 440q^{37}$$ $$\mathstrut -\mathstrut 474q^{38}$$ $$\mathstrut -\mathstrut 462q^{39}$$ $$\mathstrut -\mathstrut 468q^{40}$$ $$\mathstrut -\mathstrut 428q^{41}$$ $$\mathstrut -\mathstrut 486q^{42}$$ $$\mathstrut -\mathstrut 442q^{43}$$ $$\mathstrut -\mathstrut 450q^{44}$$ $$\mathstrut -\mathstrut 462q^{45}$$ $$\mathstrut -\mathstrut 394q^{46}$$ $$\mathstrut -\mathstrut 396q^{47}$$ $$\mathstrut -\mathstrut 206q^{48}$$ $$\mathstrut -\mathstrut 381q^{49}$$ $$\mathstrut -\mathstrut 309q^{50}$$ $$\mathstrut -\mathstrut 379q^{51}$$ $$\mathstrut -\mathstrut 772q^{52}$$ $$\mathstrut -\mathstrut 348q^{53}$$ $$\mathstrut -\mathstrut 104q^{54}$$ $$\mathstrut -\mathstrut 304q^{55}$$ $$\mathstrut -\mathstrut 46q^{56}$$ $$\mathstrut -\mathstrut 148q^{57}$$ $$\mathstrut -\mathstrut 310q^{58}$$ $$\mathstrut -\mathstrut 337q^{59}$$ $$\mathstrut -\mathstrut 268q^{60}$$ $$\mathstrut -\mathstrut 332q^{61}$$ $$\mathstrut -\mathstrut 354q^{62}$$ $$\mathstrut -\mathstrut 172q^{63}$$ $$\mathstrut -\mathstrut 83q^{64}$$ $$\mathstrut -\mathstrut 316q^{65}$$ $$\mathstrut -\mathstrut 160q^{66}$$ $$\mathstrut -\mathstrut 398q^{67}$$ $$\mathstrut -\mathstrut 348q^{68}$$ $$\mathstrut -\mathstrut 670q^{69}$$ $$\mathstrut -\mathstrut 318q^{70}$$ $$\mathstrut -\mathstrut 394q^{71}$$ $$\mathstrut -\mathstrut 235q^{72}$$ $$\mathstrut -\mathstrut 354q^{73}$$ $$\mathstrut -\mathstrut 448q^{74}$$ $$\mathstrut -\mathstrut 448q^{75}$$ $$\mathstrut -\mathstrut 570q^{76}$$ $$\mathstrut -\mathstrut 518q^{77}$$ $$\mathstrut -\mathstrut 558q^{78}$$ $$\mathstrut -\mathstrut 502q^{79}$$ $$\mathstrut -\mathstrut 596q^{80}$$ $$\mathstrut -\mathstrut 545q^{81}$$ $$\mathstrut -\mathstrut 552q^{82}$$ $$\mathstrut -\mathstrut 514q^{83}$$ $$\mathstrut -\mathstrut 694q^{84}$$ $$\mathstrut -\mathstrut 445q^{85}$$ $$\mathstrut -\mathstrut 1010q^{86}$$ $$\mathstrut -\mathstrut 558q^{87}$$ $$\mathstrut -\mathstrut 610q^{88}$$ $$\mathstrut -\mathstrut 516q^{89}$$ $$\mathstrut -\mathstrut 636q^{90}$$ $$\mathstrut -\mathstrut 502q^{91}$$ $$\mathstrut -\mathstrut 510q^{92}$$ $$\mathstrut -\mathstrut 582q^{93}$$ $$\mathstrut -\mathstrut 502q^{94}$$ $$\mathstrut -\mathstrut 526q^{95}$$ $$\mathstrut -\mathstrut 618q^{96}$$ $$\mathstrut -\mathstrut 556q^{97}$$ $$\mathstrut -\mathstrut 385q^{98}$$ $$\mathstrut -\mathstrut 380q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1003))$$

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
1003.2.a $$\chi_{1003}(1, \cdot)$$ 1003.2.a.a 1 1
1003.2.a.b 1
1003.2.a.c 1
1003.2.a.d 1
1003.2.a.e 3
1003.2.a.f 4
1003.2.a.g 10
1003.2.a.h 16
1003.2.a.i 18
1003.2.a.j 22
1003.2.d $$\chi_{1003}(237, \cdot)$$ 1003.2.d.a 2 1
1003.2.d.b 4
1003.2.d.c 38
1003.2.d.d 44
1003.2.e $$\chi_{1003}(591, \cdot)$$ n/a 176 2
1003.2.g $$\chi_{1003}(60, \cdot)$$ n/a 344 4
1003.2.i $$\chi_{1003}(58, \cdot)$$ n/a 704 8
1003.2.k $$\chi_{1003}(35, \cdot)$$ n/a 2240 28
1003.2.l $$\chi_{1003}(16, \cdot)$$ n/a 2464 28
1003.2.p $$\chi_{1003}(4, \cdot)$$ n/a 4928 56
1003.2.r $$\chi_{1003}(9, \cdot)$$ n/a 9856 112
1003.2.t $$\chi_{1003}(6, \cdot)$$ n/a 19712 224

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1003))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1003)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 2}$$