Properties

Label 925.2
Level 925
Weight 2
Dimension 30759
Nonzero newspaces 36
Newform subspaces 120
Sturm bound 136800
Trace bound 4

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Defining parameters

Level: \( N \) = \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Newform subspaces: \( 120 \)
Sturm bound: \(136800\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(925))\).

Total New Old
Modular forms 35208 32193 3015
Cusp forms 33193 30759 2434
Eisenstein series 2015 1434 581

Trace form

\( 30759 q - 220 q^{2} - 222 q^{3} - 228 q^{4} - 278 q^{5} - 366 q^{6} - 230 q^{7} - 244 q^{8} - 240 q^{9} + O(q^{10}) \) \( 30759 q - 220 q^{2} - 222 q^{3} - 228 q^{4} - 278 q^{5} - 366 q^{6} - 230 q^{7} - 244 q^{8} - 240 q^{9} - 298 q^{10} - 366 q^{11} - 270 q^{12} - 242 q^{13} - 262 q^{14} - 308 q^{15} - 372 q^{16} - 230 q^{17} - 242 q^{18} - 214 q^{19} - 268 q^{20} - 366 q^{21} - 206 q^{22} - 222 q^{23} - 194 q^{24} - 258 q^{25} - 735 q^{26} - 258 q^{27} - 266 q^{28} - 252 q^{29} - 308 q^{30} - 420 q^{31} - 342 q^{32} - 306 q^{33} - 344 q^{34} - 328 q^{35} - 565 q^{36} - 299 q^{37} - 544 q^{38} - 288 q^{39} - 318 q^{40} - 440 q^{41} - 278 q^{42} - 258 q^{43} - 314 q^{44} - 238 q^{45} - 438 q^{46} - 248 q^{47} - 222 q^{48} - 242 q^{49} - 238 q^{50} - 706 q^{51} - 190 q^{52} - 232 q^{53} - 194 q^{54} - 308 q^{55} - 398 q^{56} - 214 q^{57} - 272 q^{58} - 270 q^{59} - 268 q^{60} - 431 q^{61} - 276 q^{62} - 350 q^{63} - 374 q^{64} - 298 q^{65} - 666 q^{66} - 306 q^{67} - 334 q^{68} - 410 q^{69} - 348 q^{70} - 478 q^{71} - 552 q^{72} - 372 q^{73} - 372 q^{74} - 596 q^{75} - 918 q^{76} - 318 q^{77} - 542 q^{78} - 366 q^{79} - 298 q^{80} - 576 q^{81} - 334 q^{82} - 198 q^{83} - 514 q^{84} - 218 q^{85} - 492 q^{86} - 302 q^{87} - 264 q^{88} - 189 q^{89} - 238 q^{90} - 408 q^{91} - 360 q^{92} - 264 q^{93} - 254 q^{94} - 308 q^{95} - 586 q^{96} - 202 q^{97} - 380 q^{98} - 356 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(925))\)

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
925.2.a \(\chi_{925}(1, \cdot)\) 925.2.a.a 1 1
925.2.a.b 1
925.2.a.c 1
925.2.a.d 1
925.2.a.e 1
925.2.a.f 5
925.2.a.g 5
925.2.a.h 5
925.2.a.i 5
925.2.a.j 7
925.2.a.k 7
925.2.a.l 9
925.2.a.m 9
925.2.b \(\chi_{925}(149, \cdot)\) 925.2.b.a 2 1
925.2.b.b 2
925.2.b.c 2
925.2.b.d 2
925.2.b.e 2
925.2.b.f 10
925.2.b.g 10
925.2.b.h 10
925.2.b.i 14
925.2.c \(\chi_{925}(776, \cdot)\) 925.2.c.a 2 1
925.2.c.b 2
925.2.c.c 12
925.2.c.d 12
925.2.c.e 12
925.2.c.f 16
925.2.d \(\chi_{925}(924, \cdot)\) 925.2.d.a 2 1
925.2.d.b 2
925.2.d.c 2
925.2.d.d 2
925.2.d.e 12
925.2.d.f 12
925.2.d.g 24
925.2.e \(\chi_{925}(26, \cdot)\) 925.2.e.a 2 2
925.2.e.b 14
925.2.e.c 14
925.2.e.d 24
925.2.e.e 24
925.2.e.f 36
925.2.f \(\chi_{925}(43, \cdot)\) 925.2.f.a 2 2
925.2.f.b 2
925.2.f.c 6
925.2.f.d 24
925.2.f.e 28
925.2.f.f 48
925.2.k \(\chi_{925}(68, \cdot)\) 925.2.k.a 2 2
925.2.k.b 2
925.2.k.c 6
925.2.k.d 24
925.2.k.e 28
925.2.k.f 48
925.2.l \(\chi_{925}(186, \cdot)\) 925.2.l.a 4 4
925.2.l.b 176
925.2.l.c 180
925.2.m \(\chi_{925}(249, \cdot)\) 925.2.m.a 4 2
925.2.m.b 4
925.2.m.c 28
925.2.m.d 28
925.2.m.e 48
925.2.n \(\chi_{925}(101, \cdot)\) 925.2.n.a 4 2
925.2.n.b 24
925.2.n.c 24
925.2.n.d 28
925.2.n.e 32
925.2.o \(\chi_{925}(174, \cdot)\) 925.2.o.a 4 2
925.2.o.b 28
925.2.o.c 28
925.2.o.d 48
925.2.p \(\chi_{925}(201, \cdot)\) 925.2.p.a 6 6
925.2.p.b 6
925.2.p.c 36
925.2.p.d 36
925.2.p.e 78
925.2.p.f 78
925.2.p.g 108
925.2.q \(\chi_{925}(184, \cdot)\) 925.2.q.a 368 4
925.2.r \(\chi_{925}(36, \cdot)\) 925.2.r.a 376 4
925.2.s \(\chi_{925}(334, \cdot)\) 925.2.s.a 360 4
925.2.t \(\chi_{925}(82, \cdot)\) 925.2.t.a 56 4
925.2.t.b 68
925.2.t.c 96
925.2.y \(\chi_{925}(193, \cdot)\) 925.2.y.a 56 4
925.2.y.b 68
925.2.y.c 96
925.2.z \(\chi_{925}(121, \cdot)\) 925.2.z.a 736 8
925.2.ba \(\chi_{925}(99, \cdot)\) 925.2.ba.a 36 6
925.2.ba.b 72
925.2.ba.c 72
925.2.ba.d 156
925.2.bb \(\chi_{925}(151, \cdot)\) 925.2.bb.a 18 6
925.2.bb.b 72
925.2.bb.c 78
925.2.bb.d 78
925.2.bb.e 96
925.2.bc \(\chi_{925}(49, \cdot)\) 925.2.bc.a 12 6
925.2.bc.b 12
925.2.bc.c 72
925.2.bc.d 72
925.2.bc.e 156
925.2.bd \(\chi_{925}(117, \cdot)\) 925.2.bd.a 744 8
925.2.bi \(\chi_{925}(142, \cdot)\) 925.2.bi.a 744 8
925.2.bj \(\chi_{925}(84, \cdot)\) 925.2.bj.a 752 8
925.2.bk \(\chi_{925}(11, \cdot)\) 925.2.bk.a 752 8
925.2.bl \(\chi_{925}(64, \cdot)\) 925.2.bl.a 736 8
925.2.bn \(\chi_{925}(18, \cdot)\) 925.2.bn.a 144 12
925.2.bn.b 204
925.2.bn.c 312
925.2.bq \(\chi_{925}(32, \cdot)\) 925.2.bq.a 144 12
925.2.bq.b 204
925.2.bq.c 312
925.2.bs \(\chi_{925}(16, \cdot)\) 925.2.bs.a 2208 24
925.2.bt \(\chi_{925}(8, \cdot)\) 925.2.bt.a 1488 16
925.2.by \(\chi_{925}(88, \cdot)\) 925.2.by.a 1488 16
925.2.bz \(\chi_{925}(9, \cdot)\) 925.2.bz.a 2256 24
925.2.ca \(\chi_{925}(21, \cdot)\) 925.2.ca.a 2256 24
925.2.cb \(\chi_{925}(4, \cdot)\) 925.2.cb.a 2208 24
925.2.cd \(\chi_{925}(2, \cdot)\) 925.2.cd.a 4464 48
925.2.cg \(\chi_{925}(17, \cdot)\) 925.2.cg.a 4464 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(925)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 2}\)