## Defining parameters

 Level: $$N$$ = $$983$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$161048$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(983))$$.

Total New Old
Modular forms 40753 40753 0
Cusp forms 39772 39772 0
Eisenstein series 981 981 0

## Trace form

 $$39772 q - 488 q^{2} - 487 q^{3} - 484 q^{4} - 485 q^{5} - 479 q^{6} - 483 q^{7} - 476 q^{8} - 478 q^{9} + O(q^{10})$$ $$39772 q - 488 q^{2} - 487 q^{3} - 484 q^{4} - 485 q^{5} - 479 q^{6} - 483 q^{7} - 476 q^{8} - 478 q^{9} - 473 q^{10} - 479 q^{11} - 463 q^{12} - 477 q^{13} - 467 q^{14} - 467 q^{15} - 460 q^{16} - 473 q^{17} - 452 q^{18} - 471 q^{19} - 449 q^{20} - 459 q^{21} - 455 q^{22} - 467 q^{23} - 431 q^{24} - 460 q^{25} - 449 q^{26} - 451 q^{27} - 435 q^{28} - 461 q^{29} - 419 q^{30} - 459 q^{31} - 428 q^{32} - 443 q^{33} - 437 q^{34} - 443 q^{35} - 400 q^{36} - 453 q^{37} - 431 q^{38} - 435 q^{39} - 401 q^{40} - 449 q^{41} - 395 q^{42} - 447 q^{43} - 407 q^{44} - 413 q^{45} - 419 q^{46} - 443 q^{47} - 367 q^{48} - 434 q^{49} - 398 q^{50} - 419 q^{51} - 393 q^{52} - 437 q^{53} - 371 q^{54} - 419 q^{55} - 371 q^{56} - 411 q^{57} - 401 q^{58} - 431 q^{59} - 323 q^{60} - 429 q^{61} - 395 q^{62} - 387 q^{63} - 364 q^{64} - 407 q^{65} - 347 q^{66} - 423 q^{67} - 365 q^{68} - 395 q^{69} - 347 q^{70} - 419 q^{71} - 296 q^{72} - 417 q^{73} - 377 q^{74} - 367 q^{75} - 351 q^{76} - 395 q^{77} - 323 q^{78} - 411 q^{79} - 305 q^{80} - 370 q^{81} - 365 q^{82} - 407 q^{83} - 267 q^{84} - 383 q^{85} - 359 q^{86} - 371 q^{87} - 311 q^{88} - 401 q^{89} - 257 q^{90} - 379 q^{91} - 323 q^{92} - 363 q^{93} - 347 q^{94} - 371 q^{95} - 239 q^{96} - 393 q^{97} - 320 q^{98} - 335 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(983))$$

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
983.2.a $$\chi_{983}(1, \cdot)$$ 983.2.a.a 28 1
983.2.a.b 54
983.2.c $$\chi_{983}(2, \cdot)$$ 983.2.c.a 39690 490