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Properties

Label 845.2
Level 845
Weight 2
Dimension 25107
Nonzero newspaces 24
Newform subspaces 122
Sturm bound 113568
Trace bound 3

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Defining parameters

Level: \( N \) = \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 122 \)
Sturm bound: \(113568\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(845))\).

Total New Old
Modular forms 29304 26333 2971
Cusp forms 27481 25107 2374
Eisenstein series 1823 1226 597

Trace form

\( 25107 q - 129 q^{2} - 128 q^{3} - 125 q^{4} - 197 q^{5} - 384 q^{6} - 132 q^{7} - 153 q^{8} - 151 q^{9} + O(q^{10}) \) \( 25107 q - 129 q^{2} - 128 q^{3} - 125 q^{4} - 197 q^{5} - 384 q^{6} - 132 q^{7} - 153 q^{8} - 151 q^{9} - 225 q^{10} - 408 q^{11} - 208 q^{12} - 168 q^{13} - 276 q^{14} - 218 q^{15} - 445 q^{16} - 150 q^{17} - 225 q^{18} - 192 q^{19} - 257 q^{20} - 468 q^{21} - 216 q^{22} - 156 q^{23} - 312 q^{24} - 209 q^{25} - 492 q^{26} - 356 q^{27} - 276 q^{28} - 210 q^{29} - 330 q^{30} - 468 q^{31} - 333 q^{32} - 252 q^{33} - 270 q^{34} - 274 q^{35} - 641 q^{36} - 162 q^{37} - 240 q^{38} - 208 q^{39} - 507 q^{40} - 534 q^{41} - 396 q^{42} - 272 q^{43} - 360 q^{44} - 335 q^{45} - 660 q^{46} - 252 q^{47} - 248 q^{48} - 307 q^{49} - 357 q^{50} - 540 q^{51} - 226 q^{52} - 294 q^{53} - 132 q^{54} - 174 q^{55} - 444 q^{56} - 108 q^{57} - 126 q^{58} - 96 q^{59} + 82 q^{60} - 466 q^{61} - 84 q^{62} - 84 q^{63} - 89 q^{64} - 201 q^{65} - 756 q^{66} - 96 q^{67} - 138 q^{68} - 12 q^{69} - 162 q^{70} - 468 q^{71} - 105 q^{72} - 186 q^{73} - 294 q^{74} - 178 q^{75} - 528 q^{76} - 252 q^{77} - 348 q^{78} - 316 q^{79} - 389 q^{80} - 595 q^{81} - 426 q^{82} - 360 q^{83} - 492 q^{84} - 366 q^{85} - 768 q^{86} - 492 q^{87} - 648 q^{88} - 426 q^{89} - 603 q^{90} - 628 q^{91} - 660 q^{92} - 540 q^{93} - 564 q^{94} - 394 q^{95} - 1128 q^{96} - 354 q^{97} - 537 q^{98} - 576 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)

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
845.2.a \(\chi_{845}(1, \cdot)\) 845.2.a.a 1 1
845.2.a.b 2
845.2.a.c 2
845.2.a.d 2
845.2.a.e 2
845.2.a.f 2
845.2.a.g 2
845.2.a.h 3
845.2.a.i 3
845.2.a.j 3
845.2.a.k 3
845.2.a.l 4
845.2.a.m 4
845.2.a.n 9
845.2.a.o 9
845.2.b \(\chi_{845}(339, \cdot)\) 845.2.b.a 2 1
845.2.b.b 2
845.2.b.c 6
845.2.b.d 6
845.2.b.e 6
845.2.b.f 8
845.2.b.g 18
845.2.b.h 18
845.2.c \(\chi_{845}(506, \cdot)\) 845.2.c.a 2 1
845.2.c.b 4
845.2.c.c 4
845.2.c.d 4
845.2.c.e 4
845.2.c.f 6
845.2.c.g 8
845.2.c.h 18
845.2.d \(\chi_{845}(844, \cdot)\) 845.2.d.a 6 1
845.2.d.b 6
845.2.d.c 8
845.2.d.d 12
845.2.d.e 36
845.2.e \(\chi_{845}(146, \cdot)\) 845.2.e.a 2 2
845.2.e.b 2
845.2.e.c 4
845.2.e.d 4
845.2.e.e 4
845.2.e.f 4
845.2.e.g 4
845.2.e.h 4
845.2.e.i 6
845.2.e.j 6
845.2.e.k 6
845.2.e.l 6
845.2.e.m 8
845.2.e.n 8
845.2.e.o 18
845.2.e.p 18
845.2.f \(\chi_{845}(408, \cdot)\) 845.2.f.a 2 2
845.2.f.b 8
845.2.f.c 12
845.2.f.d 20
845.2.f.e 20
845.2.f.f 72
845.2.k \(\chi_{845}(268, \cdot)\) 845.2.k.a 2 2
845.2.k.b 8
845.2.k.c 12
845.2.k.d 20
845.2.k.e 20
845.2.k.f 72
845.2.l \(\chi_{845}(654, \cdot)\) 845.2.l.a 4 2
845.2.l.b 4
845.2.l.c 8
845.2.l.d 12
845.2.l.e 12
845.2.l.f 24
845.2.l.g 72
845.2.m \(\chi_{845}(316, \cdot)\) 845.2.m.a 4 2
845.2.m.b 4
845.2.m.c 4
845.2.m.d 8
845.2.m.e 8
845.2.m.f 8
845.2.m.g 8
845.2.m.h 12
845.2.m.i 12
845.2.m.j 36
845.2.n \(\chi_{845}(484, \cdot)\) 845.2.n.a 4 2
845.2.n.b 4
845.2.n.c 8
845.2.n.d 8
845.2.n.e 12
845.2.n.f 12
845.2.n.g 12
845.2.n.h 36
845.2.n.i 36
845.2.o \(\chi_{845}(258, \cdot)\) 845.2.o.a 4 4
845.2.o.b 4
845.2.o.c 16
845.2.o.d 16
845.2.o.e 20
845.2.o.f 20
845.2.o.g 20
845.2.o.h 24
845.2.o.i 144
845.2.t \(\chi_{845}(188, \cdot)\) 845.2.t.a 4 4
845.2.t.b 4
845.2.t.c 16
845.2.t.d 16
845.2.t.e 20
845.2.t.f 20
845.2.t.g 20
845.2.t.h 24
845.2.t.i 144
845.2.u \(\chi_{845}(66, \cdot)\) 845.2.u.a 372 12
845.2.u.b 372
845.2.v \(\chi_{845}(64, \cdot)\) 845.2.v.a 1056 12
845.2.w \(\chi_{845}(51, \cdot)\) 845.2.w.a 744 12
845.2.x \(\chi_{845}(14, \cdot)\) 845.2.x.a 1080 12
845.2.y \(\chi_{845}(16, \cdot)\) 845.2.y.a 720 24
845.2.y.b 720
845.2.z \(\chi_{845}(8, \cdot)\) 845.2.z.a 2136 24
845.2.be \(\chi_{845}(18, \cdot)\) 845.2.be.a 2136 24
845.2.bf \(\chi_{845}(9, \cdot)\) 845.2.bf.a 2160 24
845.2.bg \(\chi_{845}(36, \cdot)\) 845.2.bg.a 1440 24
845.2.bh \(\chi_{845}(4, \cdot)\) 845.2.bh.a 2112 24
845.2.bi \(\chi_{845}(7, \cdot)\) 845.2.bi.a 4272 48
845.2.bn \(\chi_{845}(2, \cdot)\) 845.2.bn.a 4272 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(845))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(845)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 1}\)