# Properties

 Label 3724.1 Level 3724 Weight 1 Dimension 65 Nonzero newspaces 7 Newform subspaces 16 Sturm bound 846720 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$3724 = 2^{2} \cdot 7^{2} \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$16$$ Sturm bound: $$846720$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3724))$$.

Total New Old
Modular forms 5624 1713 3911
Cusp forms 224 65 159
Eisenstein series 5400 1648 3752

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 49 16 0 0

## Trace form

 $$65q + 2q^{4} + 5q^{5} - 4q^{6} + q^{9} + O(q^{10})$$ $$65q + 2q^{4} + 5q^{5} - 4q^{6} + q^{9} + 5q^{11} - 4q^{13} - 2q^{16} + q^{17} + q^{19} - 8q^{22} - 10q^{23} - 2q^{24} + 8q^{25} - 8q^{29} - 2q^{33} - 6q^{35} + 4q^{37} - 2q^{38} + 4q^{41} - q^{43} - 16q^{45} - 4q^{46} + 5q^{47} - 2q^{52} + 2q^{54} - 8q^{55} - 8q^{57} + 3q^{61} - 4q^{62} - 16q^{64} + 4q^{68} + 8q^{69} + 7q^{73} - 8q^{78} + 3q^{81} + 2q^{83} + q^{85} + 2q^{86} - 4q^{88} + 2q^{89} + 2q^{93} + 4q^{94} + 5q^{95} - 4q^{96} - 4q^{97} - q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3724))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
3724.1.b $$\chi_{3724}(3723, \cdot)$$ None 0 1
3724.1.c $$\chi_{3724}(685, \cdot)$$ None 0 1
3724.1.d $$\chi_{3724}(1863, \cdot)$$ None 0 1
3724.1.e $$\chi_{3724}(1177, \cdot)$$ 3724.1.e.a 1 1
3724.1.e.b 1
3724.1.e.c 1
3724.1.e.d 1
3724.1.e.e 1
3724.1.m $$\chi_{3724}(753, \cdot)$$ None 0 2
3724.1.n $$\chi_{3724}(1831, \cdot)$$ 3724.1.n.a 4 2
3724.1.o $$\chi_{3724}(1109, \cdot)$$ None 0 2
3724.1.p $$\chi_{3724}(31, \cdot)$$ None 0 2
3724.1.z $$\chi_{3724}(1489, \cdot)$$ None 0 2
3724.1.ba $$\chi_{3724}(411, \cdot)$$ None 0 2
3724.1.bb $$\chi_{3724}(2059, \cdot)$$ 3724.1.bb.a 4 2
3724.1.bb.b 4
3724.1.bc $$\chi_{3724}(569, \cdot)$$ 3724.1.bc.a 2 2
3724.1.bc.b 2
3724.1.bc.c 2
3724.1.bc.d 2
3724.1.bd $$\chi_{3724}(1255, \cdot)$$ None 0 2
3724.1.be $$\chi_{3724}(981, \cdot)$$ None 0 2
3724.1.bf $$\chi_{3724}(2155, \cdot)$$ None 0 2
3724.1.bg $$\chi_{3724}(913, \cdot)$$ None 0 2
3724.1.bh $$\chi_{3724}(227, \cdot)$$ None 0 2
3724.1.bi $$\chi_{3724}(881, \cdot)$$ None 0 2
3724.1.bj $$\chi_{3724}(373, \cdot)$$ None 0 2
3724.1.bk $$\chi_{3724}(1451, \cdot)$$ 3724.1.bk.a 4 2
3724.1.bv $$\chi_{3724}(113, \cdot)$$ 3724.1.bv.a 12 6
3724.1.bw $$\chi_{3724}(267, \cdot)$$ None 0 6
3724.1.bx $$\chi_{3724}(153, \cdot)$$ None 0 6
3724.1.by $$\chi_{3724}(531, \cdot)$$ None 0 6
3724.1.cb $$\chi_{3724}(655, \cdot)$$ None 0 6
3724.1.cc $$\chi_{3724}(1207, \cdot)$$ None 0 6
3724.1.cf $$\chi_{3724}(313, \cdot)$$ None 0 6
3724.1.cg $$\chi_{3724}(1549, \cdot)$$ None 0 6
3724.1.ch $$\chi_{3724}(393, \cdot)$$ None 0 6
3724.1.ci $$\chi_{3724}(1469, \cdot)$$ None 0 6
3724.1.cn $$\chi_{3724}(263, \cdot)$$ None 0 6
3724.1.co $$\chi_{3724}(1587, \cdot)$$ None 0 6
3724.1.cp $$\chi_{3724}(979, \cdot)$$ None 0 6
3724.1.cq $$\chi_{3724}(99, \cdot)$$ None 0 6
3724.1.cs $$\chi_{3724}(1697, \cdot)$$ None 0 6
3724.1.ct $$\chi_{3724}(165, \cdot)$$ None 0 6
3724.1.db $$\chi_{3724}(11, \cdot)$$ None 0 12
3724.1.dc $$\chi_{3724}(445, \cdot)$$ None 0 12
3724.1.dd $$\chi_{3724}(125, \cdot)$$ None 0 12
3724.1.de $$\chi_{3724}(75, \cdot)$$ None 0 12
3724.1.df $$\chi_{3724}(229, \cdot)$$ None 0 12
3724.1.dg $$\chi_{3724}(27, \cdot)$$ None 0 12
3724.1.dh $$\chi_{3724}(141, \cdot)$$ None 0 12
3724.1.di $$\chi_{3724}(39, \cdot)$$ None 0 12
3724.1.dj $$\chi_{3724}(37, \cdot)$$ 3724.1.dj.a 12 12
3724.1.dj.b 12
3724.1.dk $$\chi_{3724}(239, \cdot)$$ None 0 12
3724.1.dl $$\chi_{3724}(255, \cdot)$$ None 0 12
3724.1.dm $$\chi_{3724}(353, \cdot)$$ None 0 12
3724.1.dw $$\chi_{3724}(103, \cdot)$$ None 0 12
3724.1.dx $$\chi_{3724}(45, \cdot)$$ None 0 12
3724.1.dy $$\chi_{3724}(163, \cdot)$$ None 0 12
3724.1.dz $$\chi_{3724}(65, \cdot)$$ None 0 12
3724.1.ed $$\chi_{3724}(53, \cdot)$$ None 0 36
3724.1.ee $$\chi_{3724}(5, \cdot)$$ None 0 36
3724.1.eg $$\chi_{3724}(3, \cdot)$$ None 0 36
3724.1.eh $$\chi_{3724}(23, \cdot)$$ None 0 36
3724.1.ei $$\chi_{3724}(43, \cdot)$$ None 0 36
3724.1.ej $$\chi_{3724}(167, \cdot)$$ None 0 36
3724.1.eo $$\chi_{3724}(109, \cdot)$$ None 0 36
3724.1.ep $$\chi_{3724}(17, \cdot)$$ None 0 36
3724.1.eq $$\chi_{3724}(237, \cdot)$$ None 0 36
3724.1.er $$\chi_{3724}(29, \cdot)$$ None 0 36
3724.1.eu $$\chi_{3724}(143, \cdot)$$ None 0 36
3724.1.ev $$\chi_{3724}(123, \cdot)$$ None 0 36

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3724))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3724)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(931))$$$$^{\oplus 3}$$