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Properties

Label 3721.2.s
Level $3721$
Weight $2$
Character orbit 3721.s
Rep. character $\chi_{3721}(3,\cdot)$
Character field $\Q(\zeta_{610})$
Dimension $75360$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.s (of order \(610\) and degree \(240\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3721 \)
Character field: \(\Q(\zeta_{610})\)
Sturm bound: \(630\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3721, [\chi])\).

Total New Old
Modular forms 75840 75840 0
Cusp forms 75360 75360 0
Eisenstein series 480 480 0

Trace form

\( 75360 q - 239 q^{2} - 243 q^{3} - 557 q^{4} - 244 q^{5} - 229 q^{6} - 254 q^{7} - 239 q^{8} + 65 q^{9} + O(q^{10}) \) \( 75360 q - 239 q^{2} - 243 q^{3} - 557 q^{4} - 244 q^{5} - 229 q^{6} - 254 q^{7} - 239 q^{8} + 65 q^{9} - 239 q^{10} - 244 q^{11} - 244 q^{12} - 232 q^{13} - 348 q^{14} - 231 q^{15} + 47 q^{16} - 244 q^{17} - 234 q^{18} - 247 q^{19} - 231 q^{20} - 244 q^{21} - 263 q^{22} - 229 q^{23} - 254 q^{24} + 68 q^{25} - 254 q^{26} - 240 q^{27} - 279 q^{28} - 244 q^{29} - 289 q^{30} - 229 q^{31} - 244 q^{32} - 269 q^{33} - 230 q^{34} - 254 q^{35} - 591 q^{36} - 239 q^{37} - 229 q^{38} - 241 q^{39} - 244 q^{40} - 256 q^{41} + 2455 q^{42} - 341 q^{43} - 438 q^{44} - 646 q^{45} - 584 q^{46} - 250 q^{47} - 192 q^{48} - 524 q^{49} - 244 q^{50} - 294 q^{51} - 206 q^{52} - 224 q^{53} - 224 q^{54} - 264 q^{55} - 216 q^{56} - 2185 q^{57} - 195 q^{58} - 5 q^{59} - 258 q^{60} + 297 q^{61} - 284 q^{62} - 239 q^{63} - 571 q^{64} - 270 q^{65} - 2217 q^{66} - 189 q^{67} - 324 q^{68} - 229 q^{69} - 221 q^{70} - 194 q^{71} - 1037 q^{72} - 233 q^{73} - 268 q^{74} - 156 q^{75} - 217 q^{76} - 667 q^{77} - 294 q^{78} - 284 q^{79} - 866 q^{80} + 85 q^{81} + 244 q^{82} - 275 q^{83} - 219 q^{84} + 311 q^{85} - 273 q^{86} + 219 q^{87} - 279 q^{88} - 304 q^{89} - 854 q^{90} - 229 q^{91} - 239 q^{92} - 244 q^{93} - 309 q^{94} - 48 q^{95} + 757 q^{96} - 295 q^{97} - 254 q^{98} - 239 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3721, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.