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Properties

Label 595.2
Level 595
Weight 2
Dimension 11615
Nonzero newspaces 36
Newform subspaces 66
Sturm bound 55296
Trace bound 14

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Defining parameters

Level: \( N \) = \( 595 = 5 \cdot 7 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Newform subspaces: \( 66 \)
Sturm bound: \(55296\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(595))\).

Total New Old
Modular forms 14592 12511 2081
Cusp forms 13057 11615 1442
Eisenstein series 1535 896 639

Trace form

\( 11615 q - 43 q^{2} - 44 q^{3} - 47 q^{4} - 81 q^{5} - 156 q^{6} - 69 q^{7} - 127 q^{8} - 53 q^{9} + O(q^{10}) \) \( 11615 q - 43 q^{2} - 44 q^{3} - 47 q^{4} - 81 q^{5} - 156 q^{6} - 69 q^{7} - 127 q^{8} - 53 q^{9} - 107 q^{10} - 188 q^{11} - 164 q^{12} - 86 q^{13} - 127 q^{14} - 276 q^{15} - 319 q^{16} - 85 q^{17} - 271 q^{18} - 92 q^{19} - 191 q^{20} - 292 q^{21} - 212 q^{22} - 96 q^{23} - 164 q^{24} - 153 q^{25} - 282 q^{26} - 104 q^{27} - 147 q^{28} - 174 q^{29} - 164 q^{30} - 256 q^{31} - 183 q^{32} - 128 q^{33} - 251 q^{34} - 245 q^{35} - 603 q^{36} - 134 q^{37} - 196 q^{38} - 168 q^{39} - 255 q^{40} - 314 q^{41} - 260 q^{42} - 268 q^{43} - 412 q^{44} - 221 q^{45} - 360 q^{46} - 224 q^{47} - 436 q^{48} - 217 q^{49} - 387 q^{50} - 300 q^{51} - 362 q^{52} - 270 q^{53} - 496 q^{54} - 260 q^{55} - 531 q^{56} - 480 q^{57} - 290 q^{58} - 260 q^{59} - 420 q^{60} - 318 q^{61} - 336 q^{62} - 273 q^{63} - 143 q^{64} - 206 q^{65} - 512 q^{66} - 76 q^{67} - 207 q^{68} - 304 q^{69} + 49 q^{70} - 424 q^{71} - 131 q^{72} - 2 q^{73} + 62 q^{74} - 76 q^{75} + 36 q^{76} - 100 q^{77} - 152 q^{78} + 72 q^{79} + 249 q^{80} - 153 q^{81} + 186 q^{82} - 92 q^{83} - 36 q^{84} - 41 q^{85} - 516 q^{86} - 40 q^{87} + 244 q^{88} - 106 q^{89} + q^{90} - 310 q^{91} - 120 q^{92} - 128 q^{93} - 120 q^{94} - 28 q^{95} - 28 q^{96} + 6 q^{97} - 315 q^{98} - 172 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)

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
595.2.a \(\chi_{595}(1, \cdot)\) 595.2.a.a 1 1
595.2.a.b 1
595.2.a.c 1
595.2.a.d 3
595.2.a.e 3
595.2.a.f 3
595.2.a.g 3
595.2.a.h 3
595.2.a.i 4
595.2.a.j 4
595.2.a.k 5
595.2.c \(\chi_{595}(239, \cdot)\) 595.2.c.a 14 1
595.2.c.b 34
595.2.d \(\chi_{595}(169, \cdot)\) 595.2.d.a 26 1
595.2.d.b 26
595.2.f \(\chi_{595}(526, \cdot)\) 595.2.f.a 2 1
595.2.f.b 12
595.2.f.c 22
595.2.i \(\chi_{595}(86, \cdot)\) 595.2.i.a 2 2
595.2.i.b 2
595.2.i.c 2
595.2.i.d 2
595.2.i.e 4
595.2.i.f 4
595.2.i.g 4
595.2.i.h 12
595.2.i.i 14
595.2.i.j 18
595.2.i.k 24
595.2.k \(\chi_{595}(106, \cdot)\) 595.2.k.a 28 2
595.2.k.b 44
595.2.l \(\chi_{595}(132, \cdot)\) 595.2.l.a 136 2
595.2.o \(\chi_{595}(188, \cdot)\) 595.2.o.a 128 2
595.2.p \(\chi_{595}(118, \cdot)\) 595.2.p.a 40 2
595.2.p.b 96
595.2.r \(\chi_{595}(13, \cdot)\) 595.2.r.a 136 2
595.2.t \(\chi_{595}(64, \cdot)\) 595.2.t.a 104 2
595.2.x \(\chi_{595}(16, \cdot)\) 595.2.x.a 4 2
595.2.x.b 92
595.2.z \(\chi_{595}(254, \cdot)\) 595.2.z.a 136 2
595.2.ba \(\chi_{595}(324, \cdot)\) 595.2.ba.a 4 2
595.2.ba.b 124
595.2.bd \(\chi_{595}(202, \cdot)\) 595.2.bd.a 272 4
595.2.bf \(\chi_{595}(36, \cdot)\) 595.2.bf.a 56 4
595.2.bf.b 88
595.2.bg \(\chi_{595}(134, \cdot)\) 595.2.bg.a 224 4
595.2.bj \(\chi_{595}(83, \cdot)\) 595.2.bj.a 272 4
595.2.bk \(\chi_{595}(4, \cdot)\) 595.2.bk.a 272 4
595.2.bn \(\chi_{595}(157, \cdot)\) 595.2.bn.a 272 4
595.2.bo \(\chi_{595}(52, \cdot)\) 595.2.bo.a 256 4
595.2.br \(\chi_{595}(33, \cdot)\) 595.2.br.a 272 4
595.2.bt \(\chi_{595}(38, \cdot)\) 595.2.bt.a 272 4
595.2.bv \(\chi_{595}(81, \cdot)\) 595.2.bv.a 192 4
595.2.bw \(\chi_{595}(57, \cdot)\) 595.2.bw.a 432 8
595.2.by \(\chi_{595}(139, \cdot)\) 595.2.by.a 32 8
595.2.by.b 512
595.2.cb \(\chi_{595}(6, \cdot)\) 595.2.cb.a 384 8
595.2.cc \(\chi_{595}(22, \cdot)\) 595.2.cc.a 432 8
595.2.cf \(\chi_{595}(138, \cdot)\) 595.2.cf.a 544 8
595.2.cg \(\chi_{595}(121, \cdot)\) 595.2.cg.a 384 8
595.2.cj \(\chi_{595}(9, \cdot)\) 595.2.cj.a 544 8
595.2.cl \(\chi_{595}(87, \cdot)\) 595.2.cl.a 544 8
595.2.cm \(\chi_{595}(88, \cdot)\) 595.2.cm.a 1088 16
595.2.co \(\chi_{595}(31, \cdot)\) 595.2.co.a 768 16
595.2.cr \(\chi_{595}(24, \cdot)\) 595.2.cr.a 1088 16
595.2.cs \(\chi_{595}(23, \cdot)\) 595.2.cs.a 1088 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(595))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(595)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 1}\)