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Properties

Label 451.2
Level 451
Weight 2
Dimension 7897
Nonzero newspaces 28
Newform subspaces 34
Sturm bound 33600
Trace bound 12

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Defining parameters

Level: \( N \) = \( 451 = 11 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Newform subspaces: \( 34 \)
Sturm bound: \(33600\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(451))\).

Total New Old
Modular forms 8800 8601 199
Cusp forms 8001 7897 104
Eisenstein series 799 704 95

Trace form

\( 7897 q - 159 q^{2} - 162 q^{3} - 171 q^{4} - 168 q^{5} - 176 q^{6} - 164 q^{7} - 175 q^{8} - 169 q^{9} + O(q^{10}) \) \( 7897 q - 159 q^{2} - 162 q^{3} - 171 q^{4} - 168 q^{5} - 176 q^{6} - 164 q^{7} - 175 q^{8} - 169 q^{9} - 174 q^{10} - 183 q^{11} - 384 q^{12} - 182 q^{13} - 192 q^{14} - 182 q^{15} - 183 q^{16} - 174 q^{17} - 207 q^{18} - 180 q^{19} - 206 q^{20} - 196 q^{21} - 179 q^{22} - 382 q^{23} - 220 q^{24} - 183 q^{25} - 186 q^{26} - 210 q^{27} - 208 q^{28} - 190 q^{29} - 156 q^{30} - 166 q^{31} - 99 q^{32} - 122 q^{33} - 322 q^{34} - 124 q^{35} + 37 q^{36} - 84 q^{37} - 140 q^{38} - 48 q^{39} + 30 q^{40} - 153 q^{41} - 88 q^{42} - 152 q^{43} - 71 q^{44} - 274 q^{45} - 156 q^{46} - 104 q^{47} - 12 q^{48} - 131 q^{49} - 169 q^{50} - 116 q^{51} - 134 q^{52} - 162 q^{53} - 180 q^{54} - 188 q^{55} - 480 q^{56} - 240 q^{57} - 250 q^{58} - 230 q^{59} - 324 q^{60} - 246 q^{61} - 228 q^{62} - 272 q^{63} - 271 q^{64} - 232 q^{65} - 116 q^{66} - 294 q^{67} - 78 q^{68} - 98 q^{69} + 88 q^{70} - 66 q^{71} + 5 q^{72} - 82 q^{73} - 22 q^{74} + 28 q^{75} + 300 q^{76} - 104 q^{77} - 144 q^{78} - 60 q^{79} + 142 q^{80} + 97 q^{81} + 181 q^{82} - 232 q^{83} + 168 q^{84} + 76 q^{85} + 84 q^{86} - 120 q^{87} + 5 q^{88} - 320 q^{89} + 198 q^{90} + 64 q^{91} - 84 q^{92} - 114 q^{93} + 88 q^{94} - 120 q^{95} + 4 q^{96} - 84 q^{97} - 143 q^{98} - 129 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(451))\)

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
451.2.a \(\chi_{451}(1, \cdot)\) 451.2.a.a 1 1
451.2.a.b 5
451.2.a.c 5
451.2.a.d 10
451.2.a.e 12
451.2.d \(\chi_{451}(122, \cdot)\) 451.2.d.a 36 1
451.2.e \(\chi_{451}(155, \cdot)\) 451.2.e.a 68 2
451.2.g \(\chi_{451}(42, \cdot)\) 451.2.g.a 64 4
451.2.g.b 96
451.2.h \(\chi_{451}(59, \cdot)\) 451.2.h.a 160 4
451.2.i \(\chi_{451}(92, \cdot)\) 451.2.i.a 160 4
451.2.j \(\chi_{451}(119, \cdot)\) 451.2.j.a 160 4
451.2.k \(\chi_{451}(78, \cdot)\) 451.2.k.a 72 4
451.2.k.b 72
451.2.l \(\chi_{451}(16, \cdot)\) 451.2.l.a 160 4
451.2.m \(\chi_{451}(109, \cdot)\) 451.2.m.a 160 4
451.2.q \(\chi_{451}(23, \cdot)\) 451.2.q.a 144 4
451.2.r \(\chi_{451}(168, \cdot)\) 451.2.r.a 160 4
451.2.s \(\chi_{451}(25, \cdot)\) 451.2.s.a 160 4
451.2.t \(\chi_{451}(81, \cdot)\) 451.2.t.a 160 4
451.2.u \(\chi_{451}(86, \cdot)\) 451.2.u.a 160 4
451.2.bf \(\chi_{451}(4, \cdot)\) 451.2.bf.a 160 4
451.2.bg \(\chi_{451}(169, \cdot)\) 451.2.bg.a 320 8
451.2.bm \(\chi_{451}(49, \cdot)\) 451.2.bm.a 320 8
451.2.bn \(\chi_{451}(144, \cdot)\) 451.2.bn.a 272 8
451.2.bo \(\chi_{451}(20, \cdot)\) 451.2.bo.a 320 8
451.2.bp \(\chi_{451}(5, \cdot)\) 451.2.bp.a 320 8
451.2.bq \(\chi_{451}(9, \cdot)\) 451.2.bq.a 320 8
451.2.bt \(\chi_{451}(13, \cdot)\) 451.2.bt.a 640 16
451.2.bu \(\chi_{451}(68, \cdot)\) 451.2.bu.a 640 16
451.2.bz \(\chi_{451}(7, \cdot)\) 451.2.bz.a 640 16
451.2.ca \(\chi_{451}(6, \cdot)\) 451.2.ca.a 640 16
451.2.cb \(\chi_{451}(19, \cdot)\) 451.2.cb.a 640 16
451.2.cc \(\chi_{451}(54, \cdot)\) 451.2.cc.a 640 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(451))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(451)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(451))\)\(^{\oplus 1}\)