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Properties

Label 3721.2
Level 3721
Weight 2
Dimension 573774
Nonzero newspaces 16
Sturm bound 2307020
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3721 = 61^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(2307020\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3721))\).

Total New Old
Modular forms 579485 579115 370
Cusp forms 574026 573774 252
Eisenstein series 5459 5341 118

Trace form

\( 573774 q - 1773 q^{2} - 1774 q^{3} - 1777 q^{4} - 1776 q^{5} - 1782 q^{6} - 1778 q^{7} - 1785 q^{8} - 1783 q^{9} + O(q^{10}) \) \( 573774 q - 1773 q^{2} - 1774 q^{3} - 1777 q^{4} - 1776 q^{5} - 1782 q^{6} - 1778 q^{7} - 1785 q^{8} - 1783 q^{9} - 1788 q^{10} - 1782 q^{11} - 1798 q^{12} - 1784 q^{13} - 1794 q^{14} - 1794 q^{15} - 1801 q^{16} - 1788 q^{17} - 1809 q^{18} - 1790 q^{19} - 1812 q^{20} - 1802 q^{21} - 1806 q^{22} - 1794 q^{23} - 1830 q^{24} - 1801 q^{25} - 1812 q^{26} - 1810 q^{27} - 1826 q^{28} - 1800 q^{29} - 1842 q^{30} - 1802 q^{31} - 1833 q^{32} - 1818 q^{33} - 1824 q^{34} - 1818 q^{35} - 1861 q^{36} - 1808 q^{37} - 1830 q^{38} - 1826 q^{39} - 1860 q^{40} - 1812 q^{41} - 1866 q^{42} - 1814 q^{43} - 1854 q^{44} - 1848 q^{45} - 1842 q^{46} - 1758 q^{47} - 1694 q^{48} - 1687 q^{49} - 1713 q^{50} - 1722 q^{51} - 1418 q^{52} - 1764 q^{53} - 1530 q^{54} - 1602 q^{55} - 1530 q^{56} - 1610 q^{57} - 1620 q^{58} - 1710 q^{59} - 1398 q^{60} - 1670 q^{61} - 3246 q^{62} - 1614 q^{63} - 1417 q^{64} - 1734 q^{65} - 1674 q^{66} - 1598 q^{67} - 1536 q^{68} - 1626 q^{69} - 1554 q^{70} - 1782 q^{71} - 1515 q^{72} - 1724 q^{73} - 1734 q^{74} - 1754 q^{75} - 1710 q^{76} - 1806 q^{77} - 1938 q^{78} - 1850 q^{79} - 1956 q^{80} - 1891 q^{81} - 1896 q^{82} - 1854 q^{83} - 1994 q^{84} - 1878 q^{85} - 1902 q^{86} - 1890 q^{87} - 1950 q^{88} - 1860 q^{89} - 2004 q^{90} - 1882 q^{91} - 1938 q^{92} - 1898 q^{93} - 1914 q^{94} - 1890 q^{95} - 2022 q^{96} - 1868 q^{97} - 1941 q^{98} - 1926 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3721))\)

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
3721.2.a \(\chi_{3721}(1, \cdot)\) 3721.2.a.a 1 1
3721.2.a.b 2
3721.2.a.c 3
3721.2.a.d 4
3721.2.a.e 4
3721.2.a.f 4
3721.2.a.g 6
3721.2.a.h 6
3721.2.a.i 8
3721.2.a.j 16
3721.2.a.k 16
3721.2.a.l 16
3721.2.a.m 40
3721.2.a.n 75
3721.2.a.o 75
3721.2.b \(\chi_{3721}(3720, \cdot)\) n/a 276 1
3721.2.c \(\chi_{3721}(1660, \cdot)\) n/a 552 2
3721.2.e \(\chi_{3721}(264, \cdot)\) n/a 1108 4
3721.2.f \(\chi_{3721}(1661, \cdot)\) n/a 550 2
3721.2.g \(\chi_{3721}(601, \cdot)\) n/a 1104 4
3721.2.i \(\chi_{3721}(574, \cdot)\) n/a 2208 8
3721.2.k \(\chi_{3721}(432, \cdot)\) n/a 2200 8
3721.2.m \(\chi_{3721}(62, \cdot)\) n/a 18780 60
3721.2.n \(\chi_{3721}(60, \cdot)\) n/a 18840 60
3721.2.o \(\chi_{3721}(13, \cdot)\) n/a 37680 120
3721.2.q \(\chi_{3721}(9, \cdot)\) n/a 75120 240
3721.2.r \(\chi_{3721}(14, \cdot)\) n/a 37800 120
3721.2.s \(\chi_{3721}(3, \cdot)\) n/a 75360 240
3721.2.u \(\chi_{3721}(12, \cdot)\) n/a 150720 480
3721.2.w \(\chi_{3721}(4, \cdot)\) n/a 151200 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3721))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3721)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3721))\)\(^{\oplus 1}\)