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Properties

Label 3019.2
Level 3019
Weight 2
Dimension 378257
Nonzero newspaces 4
Sturm bound 1519060
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3019 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1519060\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3019))\).

Total New Old
Modular forms 381274 381274 0
Cusp forms 378257 378257 0
Eisenstein series 3017 3017 0

Trace form

\( 378257 q - 1506 q^{2} - 1505 q^{3} - 1502 q^{4} - 1503 q^{5} - 1497 q^{6} - 1501 q^{7} - 1494 q^{8} - 1496 q^{9} + O(q^{10}) \) \( 378257 q - 1506 q^{2} - 1505 q^{3} - 1502 q^{4} - 1503 q^{5} - 1497 q^{6} - 1501 q^{7} - 1494 q^{8} - 1496 q^{9} - 1491 q^{10} - 1497 q^{11} - 1481 q^{12} - 1495 q^{13} - 1485 q^{14} - 1485 q^{15} - 1478 q^{16} - 1491 q^{17} - 1470 q^{18} - 1489 q^{19} - 1467 q^{20} - 1477 q^{21} - 1473 q^{22} - 1485 q^{23} - 1449 q^{24} - 1478 q^{25} - 1467 q^{26} - 1469 q^{27} - 1453 q^{28} - 1479 q^{29} - 1437 q^{30} - 1477 q^{31} - 1446 q^{32} - 1461 q^{33} - 1455 q^{34} - 1461 q^{35} - 1418 q^{36} - 1471 q^{37} - 1449 q^{38} - 1453 q^{39} - 1419 q^{40} - 1467 q^{41} - 1413 q^{42} - 1465 q^{43} - 1425 q^{44} - 1431 q^{45} - 1437 q^{46} - 1461 q^{47} - 1385 q^{48} - 1452 q^{49} - 1416 q^{50} - 1437 q^{51} - 1411 q^{52} - 1455 q^{53} - 1389 q^{54} - 1437 q^{55} - 1389 q^{56} - 1429 q^{57} - 1419 q^{58} - 1449 q^{59} - 1341 q^{60} - 1447 q^{61} - 1413 q^{62} - 1405 q^{63} - 1382 q^{64} - 1425 q^{65} - 1365 q^{66} - 1441 q^{67} - 1383 q^{68} - 1413 q^{69} - 1365 q^{70} - 1437 q^{71} - 1314 q^{72} - 1435 q^{73} - 1395 q^{74} - 1385 q^{75} - 1369 q^{76} - 1413 q^{77} - 1341 q^{78} - 1429 q^{79} - 1323 q^{80} - 1388 q^{81} - 1383 q^{82} - 1425 q^{83} - 1285 q^{84} - 1401 q^{85} - 1377 q^{86} - 1389 q^{87} - 1329 q^{88} - 1419 q^{89} - 1275 q^{90} - 1397 q^{91} - 1341 q^{92} - 1381 q^{93} - 1365 q^{94} - 1389 q^{95} - 1257 q^{96} - 1411 q^{97} - 1338 q^{98} - 1353 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3019))\)

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
3019.2.a \(\chi_{3019}(1, \cdot)\) 3019.2.a.a 2 1
3019.2.a.b 119
3019.2.a.c 130
3019.2.c \(\chi_{3019}(239, \cdot)\) n/a 502 2
3019.2.e \(\chi_{3019}(9, \cdot)\) n/a 125500 502
3019.2.g \(\chi_{3019}(4, \cdot)\) n/a 252004 1004

"n/a" means that newforms for that character have not been added to the database yet