# Properties

 Label 841.2 Level 841 Weight 2 Dimension 28790 Nonzero newspaces 8 Newform subspaces 51 Sturm bound 117740 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$841 = 29^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$51$$ Sturm bound: $$117740$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(841))$$.

Total New Old
Modular forms 30037 29939 98
Cusp forms 28834 28790 44
Eisenstein series 1203 1149 54

## Trace form

 $$28790 q - 381 q^{2} - 382 q^{3} - 385 q^{4} - 384 q^{5} - 390 q^{6} - 386 q^{7} - 393 q^{8} - 391 q^{9} + O(q^{10})$$ $$28790 q - 381 q^{2} - 382 q^{3} - 385 q^{4} - 384 q^{5} - 390 q^{6} - 386 q^{7} - 393 q^{8} - 391 q^{9} - 396 q^{10} - 390 q^{11} - 406 q^{12} - 392 q^{13} - 402 q^{14} - 402 q^{15} - 409 q^{16} - 396 q^{17} - 417 q^{18} - 398 q^{19} - 378 q^{20} - 354 q^{21} - 358 q^{22} - 374 q^{23} - 270 q^{24} - 353 q^{25} - 350 q^{26} - 334 q^{27} - 294 q^{28} - 364 q^{29} - 646 q^{30} - 354 q^{31} - 329 q^{32} - 342 q^{33} - 362 q^{34} - 370 q^{35} - 301 q^{36} - 388 q^{37} - 382 q^{38} - 378 q^{39} - 426 q^{40} - 420 q^{41} - 474 q^{42} - 422 q^{43} - 434 q^{44} - 386 q^{45} - 310 q^{46} - 370 q^{47} - 278 q^{48} - 323 q^{49} - 275 q^{50} - 338 q^{51} - 252 q^{52} - 306 q^{53} - 246 q^{54} - 226 q^{55} - 246 q^{56} - 318 q^{57} - 224 q^{58} - 746 q^{59} - 154 q^{60} - 328 q^{61} - 278 q^{62} - 258 q^{63} - 253 q^{64} - 336 q^{65} - 298 q^{66} - 334 q^{67} - 308 q^{68} - 362 q^{69} - 242 q^{70} - 310 q^{71} - 265 q^{72} - 326 q^{73} - 296 q^{74} - 362 q^{75} - 294 q^{76} - 334 q^{77} - 322 q^{78} - 402 q^{79} - 172 q^{80} - 275 q^{81} - 392 q^{82} - 350 q^{83} - 182 q^{84} - 318 q^{85} - 202 q^{86} - 322 q^{87} - 586 q^{88} - 328 q^{89} - 248 q^{90} - 322 q^{91} - 210 q^{92} - 394 q^{93} - 410 q^{94} - 274 q^{95} - 154 q^{96} - 322 q^{97} - 185 q^{98} - 170 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(841))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
841.2.a $$\chi_{841}(1, \cdot)$$ 841.2.a.a 2 1
841.2.a.b 2
841.2.a.c 2
841.2.a.d 2
841.2.a.e 3
841.2.a.f 3
841.2.a.g 6
841.2.a.h 6
841.2.a.i 8
841.2.a.j 8
841.2.a.k 12
841.2.b $$\chi_{841}(840, \cdot)$$ 841.2.b.a 4 1
841.2.b.b 4
841.2.b.c 6
841.2.b.d 12
841.2.b.e 12
841.2.b.f 16
841.2.d $$\chi_{841}(190, \cdot)$$ 841.2.d.a 6 6
841.2.d.b 6
841.2.d.c 6
841.2.d.d 6
841.2.d.e 6
841.2.d.f 12
841.2.d.g 12
841.2.d.h 12
841.2.d.i 12
841.2.d.j 12
841.2.d.k 24
841.2.d.l 24
841.2.d.m 24
841.2.d.n 36
841.2.d.o 36
841.2.d.p 48
841.2.d.q 48
841.2.e $$\chi_{841}(63, \cdot)$$ 841.2.e.a 12 6
841.2.e.b 12
841.2.e.c 12
841.2.e.d 12
841.2.e.e 12
841.2.e.f 12
841.2.e.g 12
841.2.e.h 12
841.2.e.i 12
841.2.e.j 24
841.2.e.k 24
841.2.e.l 72
841.2.e.m 96
841.2.g $$\chi_{841}(30, \cdot)$$ 841.2.g.a 1988 28
841.2.h $$\chi_{841}(28, \cdot)$$ 841.2.h.a 2016 28
841.2.j $$\chi_{841}(7, \cdot)$$ 841.2.j.a 11928 168
841.2.k $$\chi_{841}(4, \cdot)$$ 841.2.k.a 12096 168

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(841))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(841)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(841))$$$$^{\oplus 1}$$