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Properties

Label 3481.2
Level 3481
Weight 2
Dimension 501960
Nonzero newspaces 4
Sturm bound 2018980
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3481 = 59^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2018980\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3481))\).

Total New Old
Modular forms 507297 506949 348
Cusp forms 502194 501960 234
Eisenstein series 5103 4989 114

Trace form

\( 501960 q - 1656 q^{2} - 1657 q^{3} - 1660 q^{4} - 1659 q^{5} - 1665 q^{6} - 1661 q^{7} - 1668 q^{8} - 1666 q^{9} + O(q^{10}) \) \( 501960 q - 1656 q^{2} - 1657 q^{3} - 1660 q^{4} - 1659 q^{5} - 1665 q^{6} - 1661 q^{7} - 1668 q^{8} - 1666 q^{9} - 1671 q^{10} - 1665 q^{11} - 1681 q^{12} - 1667 q^{13} - 1677 q^{14} - 1677 q^{15} - 1684 q^{16} - 1671 q^{17} - 1692 q^{18} - 1673 q^{19} - 1695 q^{20} - 1685 q^{21} - 1689 q^{22} - 1677 q^{23} - 1713 q^{24} - 1684 q^{25} - 1695 q^{26} - 1693 q^{27} - 1709 q^{28} - 1683 q^{29} - 1725 q^{30} - 1685 q^{31} - 1716 q^{32} - 1701 q^{33} - 1707 q^{34} - 1701 q^{35} - 1744 q^{36} - 1691 q^{37} - 1713 q^{38} - 1709 q^{39} - 1743 q^{40} - 1695 q^{41} - 1749 q^{42} - 1697 q^{43} - 1737 q^{44} - 1673 q^{45} - 1609 q^{46} - 1643 q^{47} - 1429 q^{48} - 1594 q^{49} - 1514 q^{50} - 1493 q^{51} - 1519 q^{52} - 1591 q^{53} - 1367 q^{54} - 1551 q^{55} - 1309 q^{56} - 1443 q^{57} - 1569 q^{58} - 1624 q^{59} - 2749 q^{60} - 1599 q^{61} - 1633 q^{62} - 1467 q^{63} - 1316 q^{64} - 1563 q^{65} - 1391 q^{66} - 1605 q^{67} - 1547 q^{68} - 1517 q^{69} - 1565 q^{70} - 1609 q^{71} - 1500 q^{72} - 1669 q^{73} - 1651 q^{74} - 1719 q^{75} - 1793 q^{76} - 1749 q^{77} - 1821 q^{78} - 1733 q^{79} - 1839 q^{80} - 1774 q^{81} - 1779 q^{82} - 1737 q^{83} - 1877 q^{84} - 1761 q^{85} - 1785 q^{86} - 1773 q^{87} - 1833 q^{88} - 1743 q^{89} - 1887 q^{90} - 1765 q^{91} - 1821 q^{92} - 1781 q^{93} - 1797 q^{94} - 1773 q^{95} - 1905 q^{96} - 1751 q^{97} - 1650 q^{98} - 1635 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3481))\)

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
3481.2.a \(\chi_{3481}(1, \cdot)\) 3481.2.a.a 2 1
3481.2.a.b 2
3481.2.a.c 3
3481.2.a.d 5
3481.2.a.e 5
3481.2.a.f 5
3481.2.a.g 6
3481.2.a.h 8
3481.2.a.i 8
3481.2.a.j 12
3481.2.a.k 12
3481.2.a.l 16
3481.2.a.m 20
3481.2.a.n 20
3481.2.a.o 20
3481.2.a.p 56
3481.2.a.q 56
3481.2.c \(\chi_{3481}(53, \cdot)\) n/a 7196 28
3481.2.e \(\chi_{3481}(60, \cdot)\) n/a 17052 58
3481.2.g \(\chi_{3481}(3, \cdot)\) n/a 477456 1624

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3481))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3481)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3481))\)\(^{\oplus 1}\)