Space of modular forms of level 3721 and weight 2

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

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 - 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

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

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