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Properties

Label 669.2
Level 669
Weight 2
Dimension 12209
Nonzero newspaces 8
Newform subspaces 23
Sturm bound 66304
Trace bound 1

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Defining parameters

Level: \( N \) = \( 669 = 3 \cdot 223 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 23 \)
Sturm bound: \(66304\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(669))\).

Total New Old
Modular forms 17020 12653 4367
Cusp forms 16133 12209 3924
Eisenstein series 887 444 443

Trace form

\( 12209 q - 3 q^{2} - 112 q^{3} - 229 q^{4} - 6 q^{5} - 114 q^{6} - 230 q^{7} - 15 q^{8} - 112 q^{9} + O(q^{10}) \) \( 12209 q - 3 q^{2} - 112 q^{3} - 229 q^{4} - 6 q^{5} - 114 q^{6} - 230 q^{7} - 15 q^{8} - 112 q^{9} - 240 q^{10} - 12 q^{11} - 118 q^{12} - 236 q^{13} - 24 q^{14} - 117 q^{15} - 253 q^{16} - 18 q^{17} - 114 q^{18} - 242 q^{19} - 42 q^{20} - 119 q^{21} - 258 q^{22} - 24 q^{23} - 126 q^{24} - 253 q^{25} - 42 q^{26} - 112 q^{27} - 278 q^{28} - 30 q^{29} - 129 q^{30} - 254 q^{31} - 63 q^{32} - 123 q^{33} - 276 q^{34} - 48 q^{35} - 118 q^{36} - 260 q^{37} - 60 q^{38} - 125 q^{39} - 312 q^{40} - 42 q^{41} - 135 q^{42} - 266 q^{43} - 84 q^{44} - 117 q^{45} - 294 q^{46} - 48 q^{47} - 142 q^{48} - 279 q^{49} - 93 q^{50} - 129 q^{51} - 320 q^{52} - 54 q^{53} - 114 q^{54} - 294 q^{55} - 120 q^{56} - 131 q^{57} - 312 q^{58} - 60 q^{59} - 153 q^{60} - 284 q^{61} - 96 q^{62} - 119 q^{63} - 349 q^{64} - 84 q^{65} - 147 q^{66} - 290 q^{67} - 126 q^{68} - 135 q^{69} - 366 q^{70} - 72 q^{71} - 126 q^{72} - 296 q^{73} - 114 q^{74} - 142 q^{75} - 362 q^{76} - 96 q^{77} - 153 q^{78} - 302 q^{79} - 186 q^{80} - 112 q^{81} - 348 q^{82} - 84 q^{83} - 167 q^{84} - 330 q^{85} - 132 q^{86} - 141 q^{87} - 402 q^{88} - 90 q^{89} - 129 q^{90} - 334 q^{91} - 168 q^{92} - 143 q^{93} - 366 q^{94} - 120 q^{95} - 174 q^{96} - 320 q^{97} - 171 q^{98} - 123 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)

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
669.2.a \(\chi_{669}(1, \cdot)\) 669.2.a.a 1 1
669.2.a.b 2
669.2.a.c 2
669.2.a.d 2
669.2.a.e 3
669.2.a.f 3
669.2.a.g 3
669.2.a.h 7
669.2.a.i 14
669.2.c \(\chi_{669}(668, \cdot)\) 669.2.c.a 72 1
669.2.e \(\chi_{669}(262, \cdot)\) 669.2.e.a 2 2
669.2.e.b 4
669.2.e.c 30
669.2.e.d 38
669.2.f \(\chi_{669}(263, \cdot)\) 669.2.f.a 2 2
669.2.f.b 144
669.2.i \(\chi_{669}(4, \cdot)\) 669.2.i.a 648 36
669.2.i.b 720
669.2.k \(\chi_{669}(26, \cdot)\) 669.2.k.a 2592 36
669.2.m \(\chi_{669}(19, \cdot)\) 669.2.m.a 1296 72
669.2.m.b 1368
669.2.p \(\chi_{669}(5, \cdot)\) 669.2.p.a 72 72
669.2.p.b 5184

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(669))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(669)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 2}\)