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Properties

Label 617.2
Level 617
Weight 2
Dimension 15555
Nonzero newspaces 12
Newform subspaces 14
Sturm bound 63448
Trace bound 2

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Defining parameters

Level: \( N \) = \( 617 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 14 \)
Sturm bound: \(63448\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(617))\).

Total New Old
Modular forms 16170 16170 0
Cusp forms 15555 15555 0
Eisenstein series 615 615 0

Trace form

\( 15555 q - 305 q^{2} - 304 q^{3} - 301 q^{4} - 302 q^{5} - 296 q^{6} - 300 q^{7} - 293 q^{8} - 295 q^{9} + O(q^{10}) \) \( 15555 q - 305 q^{2} - 304 q^{3} - 301 q^{4} - 302 q^{5} - 296 q^{6} - 300 q^{7} - 293 q^{8} - 295 q^{9} - 290 q^{10} - 296 q^{11} - 280 q^{12} - 294 q^{13} - 284 q^{14} - 284 q^{15} - 277 q^{16} - 290 q^{17} - 269 q^{18} - 288 q^{19} - 266 q^{20} - 276 q^{21} - 272 q^{22} - 284 q^{23} - 248 q^{24} - 277 q^{25} - 266 q^{26} - 268 q^{27} - 252 q^{28} - 278 q^{29} - 236 q^{30} - 276 q^{31} - 245 q^{32} - 260 q^{33} - 254 q^{34} - 260 q^{35} - 217 q^{36} - 270 q^{37} - 248 q^{38} - 252 q^{39} - 218 q^{40} - 266 q^{41} - 212 q^{42} - 264 q^{43} - 224 q^{44} - 230 q^{45} - 236 q^{46} - 260 q^{47} - 184 q^{48} - 251 q^{49} - 215 q^{50} - 236 q^{51} - 210 q^{52} - 254 q^{53} - 188 q^{54} - 236 q^{55} - 188 q^{56} - 228 q^{57} - 218 q^{58} - 248 q^{59} - 140 q^{60} - 246 q^{61} - 212 q^{62} - 204 q^{63} - 181 q^{64} - 224 q^{65} - 164 q^{66} - 240 q^{67} - 182 q^{68} - 212 q^{69} - 164 q^{70} - 236 q^{71} - 113 q^{72} - 234 q^{73} - 194 q^{74} - 184 q^{75} - 168 q^{76} - 212 q^{77} - 140 q^{78} - 228 q^{79} - 122 q^{80} - 187 q^{81} - 182 q^{82} - 224 q^{83} - 84 q^{84} - 200 q^{85} - 176 q^{86} - 188 q^{87} - 128 q^{88} - 218 q^{89} - 74 q^{90} - 196 q^{91} - 140 q^{92} - 180 q^{93} - 164 q^{94} - 188 q^{95} - 56 q^{96} - 210 q^{97} - 137 q^{98} - 152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(617))\)

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
617.2.a \(\chi_{617}(1, \cdot)\) 617.2.a.a 23 1
617.2.a.b 28
617.2.b \(\chi_{617}(616, \cdot)\) 617.2.b.a 50 1
617.2.c \(\chi_{617}(194, \cdot)\) 617.2.c.a 2 2
617.2.c.b 100
617.2.d \(\chi_{617}(142, \cdot)\) 617.2.d.a 300 6
617.2.f \(\chi_{617}(31, \cdot)\) 617.2.f.a 500 10
617.2.g \(\chi_{617}(62, \cdot)\) 617.2.g.a 300 6
617.2.h \(\chi_{617}(128, \cdot)\) 617.2.h.a 500 10
617.2.i \(\chi_{617}(36, \cdot)\) 617.2.i.a 612 12
617.2.j \(\chi_{617}(15, \cdot)\) 617.2.j.a 1020 20
617.2.l \(\chi_{617}(4, \cdot)\) 617.2.l.a 3000 60
617.2.n \(\chi_{617}(2, \cdot)\) 617.2.n.a 3000 60
617.2.o \(\chi_{617}(7, \cdot)\) 617.2.o.a 6120 120