Properties

Label 859.2
Level 859
Weight 2
Dimension 30317
Nonzero newspaces 8
Newform subspaces 9
Sturm bound 122980
Trace bound 1

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Defining parameters

Level: \( N \) = \( 859 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 9 \)
Sturm bound: \(122980\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(859))\).

Total New Old
Modular forms 31174 31174 0
Cusp forms 30317 30317 0
Eisenstein series 857 857 0

Trace form

\( 30317 q - 426 q^{2} - 425 q^{3} - 422 q^{4} - 423 q^{5} - 417 q^{6} - 421 q^{7} - 414 q^{8} - 416 q^{9} + O(q^{10}) \) \( 30317 q - 426 q^{2} - 425 q^{3} - 422 q^{4} - 423 q^{5} - 417 q^{6} - 421 q^{7} - 414 q^{8} - 416 q^{9} - 411 q^{10} - 417 q^{11} - 401 q^{12} - 415 q^{13} - 405 q^{14} - 405 q^{15} - 398 q^{16} - 411 q^{17} - 390 q^{18} - 409 q^{19} - 387 q^{20} - 397 q^{21} - 393 q^{22} - 405 q^{23} - 369 q^{24} - 398 q^{25} - 387 q^{26} - 389 q^{27} - 373 q^{28} - 399 q^{29} - 357 q^{30} - 397 q^{31} - 366 q^{32} - 381 q^{33} - 375 q^{34} - 381 q^{35} - 338 q^{36} - 391 q^{37} - 369 q^{38} - 373 q^{39} - 339 q^{40} - 387 q^{41} - 333 q^{42} - 385 q^{43} - 345 q^{44} - 351 q^{45} - 357 q^{46} - 381 q^{47} - 305 q^{48} - 372 q^{49} - 336 q^{50} - 357 q^{51} - 331 q^{52} - 375 q^{53} - 309 q^{54} - 357 q^{55} - 309 q^{56} - 349 q^{57} - 339 q^{58} - 369 q^{59} - 261 q^{60} - 367 q^{61} - 333 q^{62} - 325 q^{63} - 302 q^{64} - 345 q^{65} - 285 q^{66} - 361 q^{67} - 303 q^{68} - 333 q^{69} - 285 q^{70} - 357 q^{71} - 234 q^{72} - 355 q^{73} - 315 q^{74} - 305 q^{75} - 289 q^{76} - 333 q^{77} - 261 q^{78} - 349 q^{79} - 243 q^{80} - 308 q^{81} - 303 q^{82} - 345 q^{83} - 205 q^{84} - 321 q^{85} - 297 q^{86} - 309 q^{87} - 249 q^{88} - 339 q^{89} - 195 q^{90} - 317 q^{91} - 261 q^{92} - 301 q^{93} - 285 q^{94} - 309 q^{95} - 177 q^{96} - 331 q^{97} - 258 q^{98} - 273 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(859))\)

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
859.2.a \(\chi_{859}(1, \cdot)\) 859.2.a.a 29 1
859.2.a.b 42
859.2.c \(\chi_{859}(260, \cdot)\) 859.2.c.a 142 2
859.2.e \(\chi_{859}(13, \cdot)\) 859.2.e.a 700 10
859.2.f \(\chi_{859}(100, \cdot)\) 859.2.f.a 840 12
859.2.i \(\chi_{859}(20, \cdot)\) 859.2.i.a 1420 20
859.2.j \(\chi_{859}(33, \cdot)\) 859.2.j.a 1704 24
859.2.m \(\chi_{859}(6, \cdot)\) 859.2.m.a 8400 120
859.2.o \(\chi_{859}(4, \cdot)\) 859.2.o.a 17040 240