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Properties

Label 445.2
Level 445
Weight 2
Dimension 6995
Nonzero newspaces 16
Newform subspaces 32
Sturm bound 31680
Trace bound 5

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Defining parameters

Level: \( N \) = \( 445 = 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 32 \)
Sturm bound: \(31680\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(445))\).

Total New Old
Modular forms 8272 7519 753
Cusp forms 7569 6995 574
Eisenstein series 703 524 179

Trace form

\( 6995 q - 91 q^{2} - 92 q^{3} - 95 q^{4} - 133 q^{5} - 276 q^{6} - 96 q^{7} - 103 q^{8} - 101 q^{9} + O(q^{10}) \) \( 6995 q - 91 q^{2} - 92 q^{3} - 95 q^{4} - 133 q^{5} - 276 q^{6} - 96 q^{7} - 103 q^{8} - 101 q^{9} - 135 q^{10} - 276 q^{11} - 116 q^{12} - 102 q^{13} - 112 q^{14} - 136 q^{15} - 295 q^{16} - 106 q^{17} - 127 q^{18} - 108 q^{19} - 139 q^{20} - 296 q^{21} - 124 q^{22} - 112 q^{23} - 148 q^{24} - 133 q^{25} - 306 q^{26} - 128 q^{27} - 144 q^{28} - 118 q^{29} - 144 q^{30} - 296 q^{31} - 151 q^{32} - 136 q^{33} - 142 q^{34} - 140 q^{35} - 355 q^{36} - 126 q^{37} - 148 q^{38} - 144 q^{39} - 147 q^{40} - 306 q^{41} - 184 q^{42} - 132 q^{43} - 172 q^{44} - 145 q^{45} - 336 q^{46} - 136 q^{47} - 212 q^{48} - 145 q^{49} - 135 q^{50} - 336 q^{51} - 186 q^{52} - 142 q^{53} - 208 q^{54} - 144 q^{55} - 384 q^{56} - 168 q^{57} - 178 q^{58} - 148 q^{59} - 160 q^{60} - 326 q^{61} - 184 q^{62} - 192 q^{63} - 215 q^{64} - 146 q^{65} - 408 q^{66} - 156 q^{67} - 214 q^{68} - 184 q^{69} - 156 q^{70} - 336 q^{71} - 19 q^{72} - 74 q^{73} + 18 q^{74} + 84 q^{75} + 124 q^{76} - 8 q^{77} + 272 q^{78} + 8 q^{79} + 167 q^{80} + 55 q^{81} + 138 q^{82} + 92 q^{83} + 920 q^{84} - 18 q^{85} - 44 q^{86} + 232 q^{87} + 348 q^{88} + 175 q^{89} + 225 q^{90} - 24 q^{91} + 272 q^{92} + 224 q^{93} + 120 q^{94} - 20 q^{95} + 716 q^{96} + 78 q^{97} + 93 q^{98} + 196 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)

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
445.2.a \(\chi_{445}(1, \cdot)\) 445.2.a.a 2 1
445.2.a.b 2
445.2.a.c 2
445.2.a.d 4
445.2.a.e 4
445.2.a.f 7
445.2.a.g 8
445.2.b \(\chi_{445}(179, \cdot)\) 445.2.b.a 6 1
445.2.b.b 10
445.2.b.c 28
445.2.c \(\chi_{445}(444, \cdot)\) 445.2.c.a 44 1
445.2.d \(\chi_{445}(266, \cdot)\) 445.2.d.a 2 1
445.2.d.b 12
445.2.d.c 16
445.2.e \(\chi_{445}(34, \cdot)\) 445.2.e.a 84 2
445.2.j \(\chi_{445}(301, \cdot)\) 445.2.j.a 2 2
445.2.j.b 2
445.2.j.c 24
445.2.j.d 32
445.2.l \(\chi_{445}(12, \cdot)\) 445.2.l.a 172 4
445.2.m \(\chi_{445}(37, \cdot)\) 445.2.m.a 172 4
445.2.o \(\chi_{445}(16, \cdot)\) 445.2.o.a 140 10
445.2.o.b 160
445.2.p \(\chi_{445}(11, \cdot)\) 445.2.p.a 140 10
445.2.p.b 160
445.2.q \(\chi_{445}(44, \cdot)\) 445.2.q.a 440 10
445.2.r \(\chi_{445}(4, \cdot)\) 445.2.r.a 440 10
445.2.s \(\chi_{445}(21, \cdot)\) 445.2.s.a 280 20
445.2.s.b 320
445.2.x \(\chi_{445}(9, \cdot)\) 445.2.x.a 840 20
445.2.z \(\chi_{445}(3, \cdot)\) 445.2.z.a 1720 40
445.2.ba \(\chi_{445}(7, \cdot)\) 445.2.ba.a 1720 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 2}\)