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Properties

Label 425.3
Level 425
Weight 3
Dimension 12872
Nonzero newspaces 16
Newform subspaces 41
Sturm bound 43200
Trace bound 2

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Defining parameters

Level: \( N \) = \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 41 \)
Sturm bound: \(43200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(425))\).

Total New Old
Modular forms 14848 13488 1360
Cusp forms 13952 12872 1080
Eisenstein series 896 616 280

Trace form

\( 12872 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 108 q^{5} - 132 q^{6} - 84 q^{7} - 84 q^{8} - 84 q^{9} + O(q^{10}) \) \( 12872 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 108 q^{5} - 132 q^{6} - 84 q^{7} - 84 q^{8} - 84 q^{9} - 108 q^{10} - 92 q^{11} + 12 q^{12} - 60 q^{13} - 52 q^{14} - 108 q^{15} - 252 q^{16} - 172 q^{17} - 552 q^{18} - 308 q^{19} - 388 q^{20} - 372 q^{21} - 340 q^{22} - 180 q^{23} - 152 q^{24} - 48 q^{25} - 8 q^{26} + 240 q^{27} + 636 q^{28} + 196 q^{29} + 372 q^{30} + 212 q^{31} + 548 q^{32} + 284 q^{33} + 92 q^{34} - 16 q^{35} - 324 q^{36} - 332 q^{37} - 848 q^{38} - 900 q^{39} - 1008 q^{40} - 396 q^{41} - 1532 q^{42} - 692 q^{43} - 752 q^{44} - 748 q^{45} - 572 q^{46} - 124 q^{47} - 192 q^{48} - 72 q^{49} + 72 q^{50} - 212 q^{51} + 304 q^{52} + 348 q^{53} + 1440 q^{54} + 372 q^{55} + 412 q^{56} + 1476 q^{57} + 1424 q^{58} + 384 q^{59} + 972 q^{60} - 60 q^{61} - 520 q^{62} + 8 q^{63} - 1984 q^{64} - 848 q^{65} - 508 q^{66} - 636 q^{67} - 2246 q^{68} - 2760 q^{69} - 2540 q^{70} - 1956 q^{71} - 6512 q^{72} - 3604 q^{73} - 2960 q^{74} - 1100 q^{75} - 4296 q^{76} - 1652 q^{77} - 2936 q^{78} - 1188 q^{79} + 292 q^{80} - 2012 q^{81} - 1716 q^{82} - 640 q^{83} - 140 q^{84} - 536 q^{85} + 1228 q^{86} + 976 q^{87} + 3036 q^{88} + 1332 q^{89} + 744 q^{90} + 2260 q^{91} + 5444 q^{92} + 1384 q^{93} + 3468 q^{94} + 660 q^{95} + 5692 q^{96} + 2396 q^{97} + 3492 q^{98} + 4616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(425))\)

We only show spaces with odd 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
425.3.f \(\chi_{425}(157, \cdot)\) 425.3.f.a 24 2
425.3.f.b 32
425.3.f.c 48
425.3.g \(\chi_{425}(118, \cdot)\) 425.3.g.a 16 2
425.3.g.b 16
425.3.g.c 24
425.3.g.d 48
425.3.h \(\chi_{425}(18, \cdot)\) 425.3.h.a 24 2
425.3.h.b 32
425.3.h.c 40
425.3.i \(\chi_{425}(132, \cdot)\) 425.3.i.a 24 2
425.3.i.b 32
425.3.i.c 48
425.3.l \(\chi_{425}(32, \cdot)\) 425.3.l.a 48 4
425.3.l.b 64
425.3.l.c 96
425.3.o \(\chi_{425}(168, \cdot)\) 425.3.o.a 48 4
425.3.o.b 64
425.3.o.c 96
425.3.t \(\chi_{425}(24, \cdot)\) 425.3.t.a 8 8
425.3.t.b 8
425.3.t.c 8
425.3.t.d 8
425.3.t.e 96
425.3.t.f 96
425.3.t.g 96
425.3.t.h 96
425.3.u \(\chi_{425}(126, \cdot)\) 425.3.u.a 8 8
425.3.u.b 8
425.3.u.c 96
425.3.u.d 96
425.3.u.e 96
425.3.u.f 128
425.3.x \(\chi_{425}(38, \cdot)\) 425.3.x.a 704 8
425.3.y \(\chi_{425}(52, \cdot)\) 425.3.y.a 640 8
425.3.z \(\chi_{425}(33, \cdot)\) 425.3.z.a 704 8
425.3.ba \(\chi_{425}(13, \cdot)\) 425.3.ba.a 704 8
425.3.bc \(\chi_{425}(42, \cdot)\) 425.3.bc.a 1408 16
425.3.bf \(\chi_{425}(2, \cdot)\) 425.3.bf.a 1408 16
425.3.bh \(\chi_{425}(14, \cdot)\) 425.3.bh.a 2816 32
425.3.bi \(\chi_{425}(6, \cdot)\) 425.3.bi.a 2816 32

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(425))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(425)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 1}\)