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Properties

Label 3229.2
Level 3229
Weight 2
Dimension 432822
Nonzero newspaces 8
Sturm bound 1737740
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3229 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(1737740\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3229))\).

Total New Old
Modular forms 436049 436049 0
Cusp forms 432822 432822 0
Eisenstein series 3227 3227 0

Trace form

\( 432822 q - 1611 q^{2} - 1610 q^{3} - 1607 q^{4} - 1608 q^{5} - 1602 q^{6} - 1606 q^{7} - 1599 q^{8} - 1601 q^{9} + O(q^{10}) \) \( 432822 q - 1611 q^{2} - 1610 q^{3} - 1607 q^{4} - 1608 q^{5} - 1602 q^{6} - 1606 q^{7} - 1599 q^{8} - 1601 q^{9} - 1596 q^{10} - 1602 q^{11} - 1586 q^{12} - 1600 q^{13} - 1590 q^{14} - 1590 q^{15} - 1583 q^{16} - 1596 q^{17} - 1575 q^{18} - 1594 q^{19} - 1572 q^{20} - 1582 q^{21} - 1578 q^{22} - 1590 q^{23} - 1554 q^{24} - 1583 q^{25} - 1572 q^{26} - 1574 q^{27} - 1558 q^{28} - 1584 q^{29} - 1542 q^{30} - 1582 q^{31} - 1551 q^{32} - 1566 q^{33} - 1560 q^{34} - 1566 q^{35} - 1523 q^{36} - 1576 q^{37} - 1554 q^{38} - 1558 q^{39} - 1524 q^{40} - 1572 q^{41} - 1518 q^{42} - 1570 q^{43} - 1530 q^{44} - 1536 q^{45} - 1542 q^{46} - 1566 q^{47} - 1490 q^{48} - 1557 q^{49} - 1521 q^{50} - 1542 q^{51} - 1516 q^{52} - 1560 q^{53} - 1494 q^{54} - 1542 q^{55} - 1494 q^{56} - 1534 q^{57} - 1524 q^{58} - 1554 q^{59} - 1446 q^{60} - 1552 q^{61} - 1518 q^{62} - 1510 q^{63} - 1487 q^{64} - 1530 q^{65} - 1470 q^{66} - 1546 q^{67} - 1488 q^{68} - 1518 q^{69} - 1470 q^{70} - 1542 q^{71} - 1419 q^{72} - 1540 q^{73} - 1500 q^{74} - 1490 q^{75} - 1474 q^{76} - 1518 q^{77} - 1446 q^{78} - 1534 q^{79} - 1428 q^{80} - 1493 q^{81} - 1488 q^{82} - 1530 q^{83} - 1390 q^{84} - 1506 q^{85} - 1482 q^{86} - 1494 q^{87} - 1434 q^{88} - 1524 q^{89} - 1380 q^{90} - 1502 q^{91} - 1446 q^{92} - 1486 q^{93} - 1470 q^{94} - 1494 q^{95} - 1362 q^{96} - 1516 q^{97} - 1443 q^{98} - 1458 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3229))\)

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
3229.2.a \(\chi_{3229}(1, \cdot)\) 3229.2.a.a 1 1
3229.2.a.b 2
3229.2.a.c 123
3229.2.a.d 142
3229.2.b \(\chi_{3229}(3228, \cdot)\) n/a 268 1
3229.2.c \(\chi_{3229}(914, \cdot)\) n/a 536 2
3229.2.e \(\chi_{3229}(915, \cdot)\) n/a 538 2
3229.2.g \(\chi_{3229}(5, \cdot)\) n/a 71556 268
3229.2.h \(\chi_{3229}(4, \cdot)\) n/a 71824 268
3229.2.i \(\chi_{3229}(3, \cdot)\) n/a 143648 536
3229.2.k \(\chi_{3229}(12, \cdot)\) n/a 144184 536

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