Properties

Label 833.2
Level 833
Weight 2
Dimension 26170
Nonzero newspaces 20
Newform subspaces 89
Sturm bound 112896
Trace bound 2

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Defining parameters

Level: \( N \) = \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 89 \)
Sturm bound: \(112896\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(833))\).

Total New Old
Modular forms 29184 27624 1560
Cusp forms 27265 26170 1095
Eisenstein series 1919 1454 465

Trace form

\( 26170 q - 212 q^{2} - 214 q^{3} - 220 q^{4} - 218 q^{5} - 230 q^{6} - 260 q^{7} - 392 q^{8} - 232 q^{9} + O(q^{10}) \) \( 26170 q - 212 q^{2} - 214 q^{3} - 220 q^{4} - 218 q^{5} - 230 q^{6} - 260 q^{7} - 392 q^{8} - 232 q^{9} - 246 q^{10} - 238 q^{11} - 286 q^{12} - 242 q^{13} - 288 q^{14} - 434 q^{15} - 304 q^{16} - 253 q^{17} - 564 q^{18} - 254 q^{19} - 318 q^{20} - 302 q^{21} - 450 q^{22} - 262 q^{23} - 366 q^{24} - 296 q^{25} - 326 q^{26} - 310 q^{27} - 344 q^{28} - 442 q^{29} - 414 q^{30} - 302 q^{31} - 388 q^{32} - 342 q^{33} - 345 q^{34} - 618 q^{35} - 516 q^{36} - 258 q^{37} - 290 q^{38} - 268 q^{39} - 230 q^{40} - 250 q^{41} - 246 q^{42} - 406 q^{43} - 218 q^{44} - 204 q^{45} - 146 q^{46} - 258 q^{47} - 208 q^{48} - 176 q^{49} - 738 q^{50} - 247 q^{51} - 406 q^{52} - 274 q^{53} - 314 q^{54} - 204 q^{55} - 204 q^{56} - 534 q^{57} - 306 q^{58} - 306 q^{59} - 458 q^{60} - 296 q^{61} - 418 q^{62} - 372 q^{63} - 584 q^{64} - 450 q^{65} - 622 q^{66} - 382 q^{67} - 453 q^{68} - 758 q^{69} - 498 q^{70} - 554 q^{71} - 792 q^{72} - 454 q^{73} - 518 q^{74} - 582 q^{75} - 606 q^{76} - 414 q^{77} - 650 q^{78} - 430 q^{79} - 628 q^{80} - 384 q^{81} - 356 q^{82} - 270 q^{83} - 176 q^{84} - 517 q^{85} - 536 q^{86} - 206 q^{87} - 264 q^{88} - 290 q^{89} - 104 q^{90} - 274 q^{91} - 596 q^{92} - 54 q^{93} - 276 q^{94} - 222 q^{95} + 400 q^{96} - 256 q^{97} + 48 q^{98} - 592 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)

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
833.2.a \(\chi_{833}(1, \cdot)\) 833.2.a.a 1 1
833.2.a.b 3
833.2.a.c 3
833.2.a.d 4
833.2.a.e 4
833.2.a.f 4
833.2.a.g 5
833.2.a.h 7
833.2.a.i 7
833.2.a.j 8
833.2.a.k 8
833.2.b \(\chi_{833}(50, \cdot)\) 833.2.b.a 10 1
833.2.b.b 10
833.2.b.c 10
833.2.b.d 10
833.2.b.e 16
833.2.e \(\chi_{833}(18, \cdot)\) 833.2.e.a 2 2
833.2.e.b 2
833.2.e.c 6
833.2.e.d 8
833.2.e.e 8
833.2.e.f 8
833.2.e.g 8
833.2.e.h 10
833.2.e.i 10
833.2.e.j 14
833.2.e.k 16
833.2.e.l 16
833.2.g \(\chi_{833}(344, \cdot)\) 833.2.g.a 2 2
833.2.g.b 2
833.2.g.c 4
833.2.g.d 4
833.2.g.e 16
833.2.g.f 16
833.2.g.g 16
833.2.g.h 20
833.2.g.i 32
833.2.j \(\chi_{833}(67, \cdot)\) 833.2.j.a 20 2
833.2.j.b 20
833.2.j.c 20
833.2.j.d 20
833.2.j.e 32
833.2.k \(\chi_{833}(120, \cdot)\) 833.2.k.a 6 6
833.2.k.b 216
833.2.k.c 234
833.2.l \(\chi_{833}(246, \cdot)\) 833.2.l.a 4 4
833.2.l.b 32
833.2.l.c 32
833.2.l.d 40
833.2.l.e 40
833.2.l.f 40
833.2.l.g 40
833.2.o \(\chi_{833}(30, \cdot)\) 833.2.o.a 4 4
833.2.o.b 4
833.2.o.c 8
833.2.o.d 32
833.2.o.e 32
833.2.o.f 40
833.2.o.g 40
833.2.o.h 64
833.2.r \(\chi_{833}(169, \cdot)\) 833.2.r.a 492 6
833.2.t \(\chi_{833}(48, \cdot)\) 833.2.t.a 72 8
833.2.t.b 72
833.2.t.c 72
833.2.t.d 72
833.2.t.e 160
833.2.u \(\chi_{833}(86, \cdot)\) 833.2.u.a 420 12
833.2.u.b 468
833.2.v \(\chi_{833}(128, \cdot)\) 833.2.v.a 8 8
833.2.v.b 8
833.2.v.c 64
833.2.v.d 64
833.2.v.e 64
833.2.v.f 80
833.2.v.g 80
833.2.v.h 80
833.2.x \(\chi_{833}(64, \cdot)\) 833.2.x.a 984 12
833.2.z \(\chi_{833}(16, \cdot)\) 833.2.z.a 984 12
833.2.bc \(\chi_{833}(31, \cdot)\) 833.2.bc.a 144 16
833.2.bc.b 144
833.2.bc.c 144
833.2.bc.d 144
833.2.bc.e 160
833.2.bc.f 160
833.2.bf \(\chi_{833}(8, \cdot)\) 833.2.bf.a 1968 24
833.2.bg \(\chi_{833}(4, \cdot)\) 833.2.bg.a 1968 24
833.2.bi \(\chi_{833}(6, \cdot)\) 833.2.bi.a 3936 48
833.2.bl \(\chi_{833}(2, \cdot)\) 833.2.bl.a 3936 48
833.2.bn \(\chi_{833}(3, \cdot)\) 833.2.bn.a 7872 96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(833))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(833)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)