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Properties

Label 875.2
Level 875
Weight 2
Dimension 25856
Nonzero newspaces 18
Newform subspaces 57
Sturm bound 120000
Trace bound 7

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Defining parameters

Level: \( N \) = \( 875 = 5^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 57 \)
Sturm bound: \(120000\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(875))\).

Total New Old
Modular forms 31080 27136 3944
Cusp forms 28921 25856 3065
Eisenstein series 2159 1280 879

Trace form

\( 25856 q - 126 q^{2} - 124 q^{3} - 118 q^{4} - 160 q^{5} - 216 q^{6} - 154 q^{7} - 294 q^{8} - 106 q^{9} + O(q^{10}) \) \( 25856 q - 126 q^{2} - 124 q^{3} - 118 q^{4} - 160 q^{5} - 216 q^{6} - 154 q^{7} - 294 q^{8} - 106 q^{9} - 160 q^{10} - 216 q^{11} - 76 q^{12} - 104 q^{13} - 138 q^{14} - 400 q^{15} - 242 q^{16} - 136 q^{17} - 154 q^{18} - 172 q^{19} - 230 q^{20} - 302 q^{21} - 412 q^{22} - 164 q^{23} - 340 q^{24} - 220 q^{25} - 340 q^{26} - 208 q^{27} - 274 q^{28} - 368 q^{29} - 240 q^{30} - 280 q^{31} - 218 q^{32} - 176 q^{33} - 184 q^{34} - 210 q^{35} - 726 q^{36} - 112 q^{37} - 180 q^{38} - 240 q^{39} - 260 q^{40} - 260 q^{41} - 338 q^{42} - 420 q^{43} - 292 q^{44} - 320 q^{45} - 360 q^{46} - 208 q^{47} - 556 q^{48} - 152 q^{49} - 580 q^{50} - 416 q^{51} - 424 q^{52} - 204 q^{53} - 484 q^{54} - 240 q^{55} - 406 q^{56} - 532 q^{57} - 328 q^{58} - 260 q^{59} - 440 q^{60} - 348 q^{61} - 488 q^{62} - 334 q^{63} - 654 q^{64} - 270 q^{65} - 528 q^{66} - 252 q^{67} - 516 q^{68} - 328 q^{69} - 280 q^{70} - 652 q^{71} - 626 q^{72} - 240 q^{73} - 476 q^{74} - 320 q^{75} - 632 q^{76} - 298 q^{77} - 652 q^{78} - 228 q^{79} - 440 q^{80} - 374 q^{81} - 480 q^{82} - 452 q^{83} - 506 q^{84} - 630 q^{85} - 528 q^{86} - 472 q^{87} - 740 q^{88} - 512 q^{89} - 580 q^{90} - 430 q^{91} - 692 q^{92} - 480 q^{93} - 580 q^{94} - 320 q^{95} - 464 q^{96} - 568 q^{97} - 476 q^{98} - 628 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(875))\)

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
875.2.a \(\chi_{875}(1, \cdot)\) 875.2.a.a 2 1
875.2.a.b 2
875.2.a.c 2
875.2.a.d 2
875.2.a.e 6
875.2.a.f 6
875.2.a.g 6
875.2.a.h 6
875.2.a.i 8
875.2.a.j 8
875.2.b \(\chi_{875}(624, \cdot)\) 875.2.b.a 4 1
875.2.b.b 4
875.2.b.c 12
875.2.b.d 12
875.2.b.e 16
875.2.e \(\chi_{875}(501, \cdot)\) 875.2.e.a 4 2
875.2.e.b 4
875.2.e.c 24
875.2.e.d 28
875.2.e.e 28
875.2.e.f 40
875.2.f \(\chi_{875}(307, \cdot)\) 875.2.f.a 16 2
875.2.f.b 16
875.2.f.c 32
875.2.f.d 64
875.2.h \(\chi_{875}(176, \cdot)\) 875.2.h.a 4 4
875.2.h.b 28
875.2.h.c 32
875.2.h.d 56
875.2.h.e 56
875.2.k \(\chi_{875}(249, \cdot)\) 875.2.k.a 8 2
875.2.k.b 24
875.2.k.c 40
875.2.k.d 56
875.2.n \(\chi_{875}(99, \cdot)\) 875.2.n.a 8 4
875.2.n.b 56
875.2.n.c 56
875.2.n.d 64
875.2.o \(\chi_{875}(68, \cdot)\) 875.2.o.a 128 4
875.2.o.b 128
875.2.q \(\chi_{875}(51, \cdot)\) 875.2.q.a 144 8
875.2.q.b 288
875.2.s \(\chi_{875}(118, \cdot)\) 875.2.s.a 144 8
875.2.s.b 144
875.2.s.c 144
875.2.t \(\chi_{875}(36, \cdot)\) 875.2.t.a 760 20
875.2.t.b 760
875.2.u \(\chi_{875}(74, \cdot)\) 875.2.u.a 144 8
875.2.u.b 288
875.2.y \(\chi_{875}(29, \cdot)\) 875.2.y.a 1480 20
875.2.bb \(\chi_{875}(82, \cdot)\) 875.2.bb.a 288 16
875.2.bb.b 288
875.2.bb.c 288
875.2.bc \(\chi_{875}(11, \cdot)\) 875.2.bc.a 3920 40
875.2.bd \(\chi_{875}(13, \cdot)\) 875.2.bd.a 3920 40
875.2.bg \(\chi_{875}(4, \cdot)\) 875.2.bg.a 3920 40
875.2.bj \(\chi_{875}(3, \cdot)\) 875.2.bj.a 7840 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(875))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(875)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(875))\)\(^{\oplus 1}\)