# Properties

 Label 2365.2 Level 2365 Weight 2 Dimension 197467 Nonzero newspaces 48 Sturm bound 887040 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$2365 = 5 \cdot 11 \cdot 43$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$887040$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2365))$$.

Total New Old
Modular forms 225120 201891 23229
Cusp forms 218401 197467 20934
Eisenstein series 6719 4424 2295

## Trace form

 $$197467q - 307q^{2} - 304q^{3} - 295q^{4} - 471q^{5} - 932q^{6} - 312q^{7} - 311q^{8} - 317q^{9} + O(q^{10})$$ $$197467q - 307q^{2} - 304q^{3} - 295q^{4} - 471q^{5} - 932q^{6} - 312q^{7} - 311q^{8} - 317q^{9} - 495q^{10} - 1071q^{11} - 712q^{12} - 294q^{13} - 304q^{14} - 502q^{15} - 975q^{16} - 322q^{17} - 319q^{18} - 316q^{19} - 523q^{20} - 952q^{21} - 409q^{22} - 704q^{23} - 356q^{24} - 531q^{25} - 1002q^{26} - 316q^{27} - 368q^{28} - 326q^{29} - 568q^{30} - 960q^{31} - 495q^{32} - 510q^{33} - 966q^{34} - 624q^{35} - 1483q^{36} - 490q^{37} - 692q^{38} - 564q^{39} - 775q^{40} - 1086q^{41} - 748q^{42} - 709q^{43} - 863q^{44} - 1265q^{45} - 1168q^{46} - 276q^{47} - 756q^{48} - 361q^{49} - 583q^{50} - 1000q^{51} - 490q^{52} - 422q^{53} - 348q^{54} - 516q^{55} - 2076q^{56} - 244q^{57} - 66q^{58} - 216q^{59} - 400q^{60} - 782q^{61} - 288q^{62} - 184q^{63} - 135q^{64} - 462q^{65} - 1138q^{66} - 652q^{67} - 278q^{68} - 476q^{69} - 760q^{70} - 1180q^{71} - 1091q^{72} - 522q^{73} - 1022q^{74} - 726q^{75} - 1656q^{76} - 766q^{77} - 1904q^{78} - 752q^{79} - 1087q^{80} - 1717q^{81} - 1198q^{82} - 740q^{83} - 2024q^{84} - 840q^{85} - 1619q^{86} - 1592q^{87} - 1073q^{88} - 1042q^{89} - 1203q^{90} - 1328q^{91} - 1112q^{92} - 884q^{93} - 896q^{94} - 652q^{95} - 1744q^{96} - 686q^{97} - 591q^{98} - 513q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2365))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2365.2.a $$\chi_{2365}(1, \cdot)$$ 2365.2.a.a 1 1
2365.2.a.b 1
2365.2.a.c 1
2365.2.a.d 1
2365.2.a.e 1
2365.2.a.f 2
2365.2.a.g 2
2365.2.a.h 9
2365.2.a.i 13
2365.2.a.j 16
2365.2.a.k 17
2365.2.a.l 17
2365.2.a.m 18
2365.2.a.n 20
2365.2.a.o 20
2365.2.b $$\chi_{2365}(474, \cdot)$$ n/a 212 1
2365.2.e $$\chi_{2365}(2364, \cdot)$$ n/a 260 1
2365.2.f $$\chi_{2365}(1891, \cdot)$$ n/a 176 1
2365.2.i $$\chi_{2365}(221, \cdot)$$ n/a 296 2
2365.2.k $$\chi_{2365}(87, \cdot)$$ n/a 504 2
2365.2.m $$\chi_{2365}(1332, \cdot)$$ n/a 440 2
2365.2.n $$\chi_{2365}(861, \cdot)$$ n/a 672 4
2365.2.o $$\chi_{2365}(824, \cdot)$$ n/a 520 2
2365.2.r $$\chi_{2365}(694, \cdot)$$ n/a 440 2
2365.2.u $$\chi_{2365}(351, \cdot)$$ n/a 352 2
2365.2.v $$\chi_{2365}(441, \cdot)$$ n/a 864 6
2365.2.y $$\chi_{2365}(171, \cdot)$$ n/a 704 4
2365.2.z $$\chi_{2365}(644, \cdot)$$ n/a 1040 4
2365.2.bc $$\chi_{2365}(1334, \cdot)$$ n/a 1008 4
2365.2.bd $$\chi_{2365}(738, \cdot)$$ n/a 880 4
2365.2.bf $$\chi_{2365}(208, \cdot)$$ n/a 1040 4
2365.2.bj $$\chi_{2365}(131, \cdot)$$ n/a 1056 6
2365.2.bk $$\chi_{2365}(604, \cdot)$$ n/a 1560 6
2365.2.bn $$\chi_{2365}(914, \cdot)$$ n/a 1320 6
2365.2.bo $$\chi_{2365}(36, \cdot)$$ n/a 1408 8
2365.2.bp $$\chi_{2365}(42, \cdot)$$ n/a 2080 8
2365.2.br $$\chi_{2365}(173, \cdot)$$ n/a 2016 8
2365.2.bt $$\chi_{2365}(56, \cdot)$$ n/a 1776 12
2365.2.bu $$\chi_{2365}(428, \cdot)$$ n/a 3120 12
2365.2.bw $$\chi_{2365}(452, \cdot)$$ n/a 2640 12
2365.2.by $$\chi_{2365}(381, \cdot)$$ n/a 1408 8
2365.2.cb $$\chi_{2365}(49, \cdot)$$ n/a 2080 8
2365.2.ce $$\chi_{2365}(424, \cdot)$$ n/a 2080 8
2365.2.cf $$\chi_{2365}(16, \cdot)$$ n/a 4224 24
2365.2.cg $$\chi_{2365}(76, \cdot)$$ n/a 2112 12
2365.2.cj $$\chi_{2365}(144, \cdot)$$ n/a 2640 12
2365.2.cm $$\chi_{2365}(329, \cdot)$$ n/a 3120 12
2365.2.co $$\chi_{2365}(178, \cdot)$$ n/a 4160 16
2365.2.cq $$\chi_{2365}(37, \cdot)$$ n/a 4160 16
2365.2.cr $$\chi_{2365}(4, \cdot)$$ n/a 6240 24
2365.2.cu $$\chi_{2365}(39, \cdot)$$ n/a 6240 24
2365.2.cv $$\chi_{2365}(51, \cdot)$$ n/a 4224 24
2365.2.cz $$\chi_{2365}(12, \cdot)$$ n/a 5280 24
2365.2.db $$\chi_{2365}(142, \cdot)$$ n/a 6240 24
2365.2.dc $$\chi_{2365}(31, \cdot)$$ n/a 8448 48
2365.2.de $$\chi_{2365}(27, \cdot)$$ n/a 12480 48
2365.2.dg $$\chi_{2365}(107, \cdot)$$ n/a 12480 48
2365.2.dh $$\chi_{2365}(19, \cdot)$$ n/a 12480 48
2365.2.dk $$\chi_{2365}(9, \cdot)$$ n/a 12480 48
2365.2.dn $$\chi_{2365}(46, \cdot)$$ n/a 8448 48
2365.2.do $$\chi_{2365}(13, \cdot)$$ n/a 24960 96
2365.2.dq $$\chi_{2365}(3, \cdot)$$ n/a 24960 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2365))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2365)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(215))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(473))$$$$^{\oplus 2}$$