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Properties

Label 3721.2.u
Level $3721$
Weight $2$
Character orbit 3721.u
Rep. character $\chi_{3721}(12,\cdot)$
Character field $\Q(\zeta_{915})$
Dimension $150720$
Sturm bound $630$

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Defining parameters

Level: \( N \) \(=\) \( 3721 = 61^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3721.u (of order \(915\) and degree \(480\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3721 \)
Character field: \(\Q(\zeta_{915})\)
Sturm bound: \(630\)

Dimensions

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

Total New Old
Modular forms 151680 151680 0
Cusp forms 150720 150720 0
Eisenstein series 960 960 0

Trace form

\( 150720 q - 478 q^{2} - 484 q^{3} - 788 q^{4} - 490 q^{5} - 489 q^{6} - 489 q^{7} - 484 q^{8} + 134 q^{9} + O(q^{10}) \) \( 150720 q - 478 q^{2} - 484 q^{3} - 788 q^{4} - 490 q^{5} - 489 q^{6} - 489 q^{7} - 484 q^{8} + 134 q^{9} - 503 q^{10} - 470 q^{11} - 435 q^{12} - 488 q^{13} - 255 q^{14} - 490 q^{15} - 804 q^{16} - 464 q^{17} - 473 q^{18} - 497 q^{19} - 484 q^{20} - 485 q^{21} - 489 q^{22} - 486 q^{23} - 503 q^{24} - 826 q^{25} - 504 q^{26} - 523 q^{27} - 492 q^{28} - 484 q^{29} - 542 q^{30} - 477 q^{31} - 522 q^{32} - 453 q^{33} - 506 q^{34} - 430 q^{35} - 863 q^{36} - 474 q^{37} - 464 q^{38} - 505 q^{39} - 428 q^{40} - 499 q^{41} + 2123 q^{42} - 650 q^{43} - 761 q^{44} + 232 q^{45} - 712 q^{46} - 528 q^{47} - 499 q^{48} - 799 q^{49} - 432 q^{50} - 479 q^{51} - 405 q^{52} - 505 q^{53} - 487 q^{54} - 428 q^{55} - 386 q^{56} + 1502 q^{57} - 545 q^{58} - 721 q^{59} - 468 q^{60} - 1409 q^{61} - 462 q^{62} - 430 q^{63} + 126 q^{64} - 553 q^{65} + 1422 q^{66} - 475 q^{67} - 485 q^{68} - 456 q^{69} - 520 q^{70} - 551 q^{71} - 1299 q^{72} - 442 q^{73} - 478 q^{74} - 489 q^{75} - 551 q^{76} + 269 q^{77} - 385 q^{78} - 439 q^{79} + 780 q^{80} + 84 q^{81} - 1076 q^{82} - 527 q^{83} - 488 q^{84} + 711 q^{85} - 568 q^{86} - 993 q^{87} - 542 q^{88} - 520 q^{89} + 792 q^{90} - 558 q^{91} - 565 q^{92} - 555 q^{93} - 424 q^{94} - 779 q^{95} + 504 q^{96} - 531 q^{97} - 615 q^{98} - 457 q^{99} + O(q^{100}) \)

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.