## 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

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

## 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

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